Funny girl: The not-so silent star Oona Chaplin

Actress Oona Chaplin is splendidly, almost ludicrously international, with a background that incorporates a childhood travelling in the caravan of the international movie industry, as well as roots – or tendrils at least – in Spain, Switzerland, Cuba, Scotland, Chile and England. I write England, but I mean London, and if she were a football team she would be Arsenal, which would be entirely fitting, because she claims to support Arsenal, as does her mother, the actress Geraldine Chaplin, and as did her grandfather, the one and only Charlie Chaplin.

It's not known whether her maternal great-grandfather, the Nobel Prize-winning, New York-born playwright Eugene O'Neill was also a "Gooner" but, given O'Neill's animosity towards Charlie Chaplin, and the fact that football was probably unknown to him, it seems unlikely. The point is, however, that Oona Castilla Chaplin, to use her non-stage name, is not only extraordinarily international, she has an extraordinarily illustrious bloodline. On one side of the family is a literary titan, a man dubbed "the American Chekhov", on the other, perhaps the most instantly recognisable movie star of all time. It's a lot for a girl to live up to.

"There are some greats on my father's side as well," she says, referring to the Chilean-born cinematographer Patricio Castilla. "My dad was like this major political activist and the first person who asked for political asylum in Cuba. My grandmother is one of the women who were responsible for women having the vote in Chile."

Be that as it may, the grandparent most people are going to want to know about is Charles Spencer Chaplin, a 20th-century icon up there with Marilyn Monroe, Elvis Presley and Adolf Hitler, the man Chaplin famously lampooned in The Great Dictator. "When people say 'Charlie Chaplin' I still think now of the guy in the moustache and bowler hat and funny walk – I don't think of an old man who was my grandfather," she says. "I never met him [Chaplin died in 1977], which probably adds to the confusion. There are moments, even now, when I sort of go 'Whoa... my blood has some of that in it? It's amazing, but it kind of freaks me out sometimes."

More on Charlie Chaplin later, however, for here is his strikingly beautiful granddaughter, arriving at the Camden Lock canal-side bar, chosen because that's where she recently held her 27th birthday party, in a flurry of cheek kissing – two for me, two for the PR, two for the photographer and two for the photographer's assistant. Even in this touristy mecca of post-hippy fashion stalls she stands out as something rare and exotic, dressed in a mixture of Portobello Road vintage (she lives near Ladbroke Grove), including a belt with an outsize buckle shaped like a toucan, Zara leggings and ballet pumps – all topped off with a shawl. In fact, she looks like she's jumped out of rehearsals for a stage production of Carmen, and I'm not entirely surprised when she suddenly brandishes a Spanish fan and begins to vigorously ventilate herself against the summer heat.

Can I see anything of Charlie in her? She is dark like him, but I suspect that owes more to her Chilean ancestry. She has a dancer's way of sitting – perched like a resting ballerina, and reckons she got her hoofing feet from her grandfather. "He was an incredible dancer and I can move," she says. Did she see any other resemblance? "Only in the moustache, which I occasionally have to sort out."

Very good. So let's get the story straight – because it's a fascinating tale that drops more famous names than a David Frost drinks reception. Her grandmother, the one Oona was named after, Oona O'Neill, was the daughter of the hard-drinking playwright Eugene O'Neill – he of The Iceman Cometh and Long Day's Journey into Night. When Oona O'Neill was just 18, she had a choice of legends vying for her hand – turning down the Catcher in the Rye author JD Salinger for the 54-year-old Charlie Chaplin, becoming the promiscuous screen legend's fourth wife. It was Chaplin's happiest marriage, and together they begat eight children, starting with my subject's mother, Geraldine Chaplin.

Eugene O'Neill was horrified at the age difference (and perhaps by Chaplin's goatish reputation) and cut his daughter out of his life. In 1981, when the by now elderly Oona saw Jack Nicholson portraying her estranged papa in the film Reds, she wrote to Nicholson saying, "Thanks to you, I now can love my father," Nicholson adding "that was the best compliment I ever got".

"My grandmother died in 1991 and I was born in '86. We only met once, but I didn't speak English and she didn't speak Spanish – so we had a communication problem," says Oona the younger. "I remember she had a Siamese cat called Billy Boy – a vicious brute – and she said: 'Be careful, it'll scratch you.' But that's all I remember."

Born in Madrid, where her mother had settled in 1965 after filming Doctor Zhivago in the city, but spending half of every year of her childhood (for naturalisation purposes) in Switzerland, where Charlie Chaplin settled for tax and anti-communist witch hunt reasons in the 1950s, English is only Chaplin's third language after Spanish and French. She learned it in New York and now speaks with a non-specific Americanised accent. "I have this hybrid international school accent," she says. "I used to have a very American accent, but then being here seven years and going to Rada and having RP [received pronunciation] drilled into me, it bastardised my accent."

Her mother, Geraldine Chaplin, after a personally tempestuous but artistically fruitful 10-year relationship with the Spanish film director Carlos Saura, met her father on a film set. "They were both in relationships, but within two weeks they'd both decided to spend the rest of their lives together," says Chaplin. "I still catch them making out in the kitchen and stuff, and it's like 'Mom... get a room'."

This is what the esteemed film biographer David Thomson has written about Geraldine Chaplin, the muse of Saura and, to a lesser extent, Robert Altman. "To criticise Charlie Chaplin amounts, in some quarters, to an unforgivable heresy that marks one down as the baleful, inhuman, and anti-life anti-Charlie. I believe I would give up all of Charlie's work for Cria Cuervos (Carlos Suara's 1976 family drama), which contains a performance of the utmost emotional rigour and depth from his daughter Geraldine."

High praise indeed, even from a man so famously resistant to the "little tramp's" charms as Thomson. He had better watch out if the young Oona is about because, as she believes: "Everyone loves Charlie Chaplin and not just because he's funny but because he's fucking true and human and humanist. I'm a huge fan of his – I would beat up anyone who wasn't."

It's probably this same pugnacious blood loyalty that makes Chaplin – otherwise the airiest and cheeriest-seeming young woman – say of Carlos Saura: "We hate him. We love his films, but we hate him. I've only met him once and it was the first time my mother had seen him in 27 years or something, it was at the Paris Film Festival, and I was like, 'Mum, is that...? And she was going 'Shhh... shhh'. It was a very dramatic relationship, full of affairs and I'm sure it didn't have a good ending. But then she met my dad."

"Dad", Patricio Castilla, gave up his cinematography to support Geraldine's career, and the first 15 years of Oona's life were spent either in the care of child-minders in Madrid or Switzerland, or with her parents on movie sets across the world.

"I travelled a lot. They would ask my mother to come to Thailand for three months and say 'here's a couple of tickets, you can invite your family'. I don't think they do that anymore, do they?" I look blank – film-star hospitality not being an area of my expertise – and she proceeds to answer her own question. "Maybe they don't have the money to do that any more, but back in the day, the Eighties and Nineties, my mum would be filming in Sri Lanka and my dad and me would get to go. I was also spending a lot of time in Switzerland and in Cuba. My half-brother and sister are Cuban."

Does she feel rootless? "Absolutely not. I'm the child of the future... I think that's the way it should be – being from millions of different places and travelling – it's the best education. I don't buy things now, I buy plane tickets. The only thing I want is to make enough money to be able to travel with my children."

There are no children yet but, back in her own childhood, something must have been amiss with the constant travelling, because, by her own admission, the young Oona was a handful. And then an extraordinary decision was made concerning a jet-setting individual from such an artistic background – she was sent to Gordonstoun in the north of Scotland, the bracing, famously outward-bound public school favoured by the British Royal Family, and which The Prince of Wales dubbed "Colditz in kilts".

"I loved it," she says. "I probably shouldn't say this, because I don't want to disrepute a very good school, but I think I was probably wilder at Gordonstoun than I've ever been since." Wilder? "There was no illegality to it – I think I was quite naïve compared to a lot of students in my year. For example, I'd never kissed a boy with tongues before I went to Gordonstoun. I think British kids are far more forward than Spanish kids – certainly me. Anyway, there was an awful lot of vodka involved... and kissing with tongues."

There was also a very good drama department, and Chaplin flourished – even playing her grandfather's famous little tramp in a school production of A Midsummer Night's Dream, repeating the performance at the Edinburgh festival. "If I was asked to do that today I wouldn't," she says. "I would be embarrassed to do it – not that I think there's anything wrong with it, but I guess I'm just a bit more self-conscious now. But then back then I didn't want to be an actress, so I was 'Yeah, OK, whatever'."

In fact, Chaplin applied to university to study politics and broadcasting, simultaneously however sending in an application to Rada. "I said if they take me at Rada I'll do acting, but only if they take me at Rada... and they did. I was fucked."

Contemporaries included her great friend Gemma Arterton, whom she competed against for the Bond Girl role in Quantum of Solace ("me and 1,500 others", she adds). Arterton won the role, and Chaplin became a "gloried extra. My minute and a half of glory... I brought in a beer and then I got sort of half raped and then I ran away. It was a fun five days."

Having found acting easy when she didn't care about, it suddenly became harder when she realised this is what she really wanted to do. The subsequent trajectory has so far been lower than Arterton's – the inevitable episode of Spooks, playing a Brazilian cage dancer in the sitcom Married Single Other, a sprinkling of Euro-movies, including a horror film alongside her mother. But now Chaplin has landed a peach of a project, Abi Morgan's six-part drama The Hour – the story of the early days of BBC television news that has inevitably (it's set in the 1950s) been dubbed "The British Mad Men".

Starring Romola Garai, as Bel, the producer of the eponymous ground-breaking news programme, The Hour, Ben Whishaw as Freddie, the show's maverick reporter, and The Wire's Dominic West as Hector, its womanising anchorman, Chaplin plays Maddie, a woman described in the press notes as "Hector's spoilt beautiful wife". Having interviewed West before, I know how mischievous he can be. How did they get on? "I watched The Wire three times, so when I met Dominic I was a little bit bashful," she says. "But very quickly I realised he was kind of... I was like 'Oh, you're silly. OK, we can totally get on now. I've totally lost all respect for you, but I can really get along now... you're absolutely non-threatening to me."

"Ben [Whishaw], I could marry him. Or just have him in my cupboard and take him out from time to time and say 'you're so beautiful'. And Romola... How many times have I seen Dirty Dancing 2?" I can't imagine, Oona. "A lot. She's had a great career, but I like the silly stuff as well."

In fact Garai, Whishaw, West and Chaplin are all excellent, although Chaplin only really comes into the series later on, once Bel and Hector have begun an affair behind Maddie's back. A "British Mad Men" seems an impossible tag for any television drama to live up to – and the makers are keen to distance themselves from the comparison. The hope anyway is for it to become a returning series.

In the meantime, Chaplin is eager to get as much experience under her belt as possible. Speaking three languages fluently obviously helps, and she's keen to do a movie in France. "At the moment I'm just not saying 'no' to anybody – I am a whore – anybody can have me," she says, rather alarmingly. "So that I can gain experience and hopefully my career will define itself."

When not filming or auditioning she lives in the shadow of the Westway in Notting Hill, her neighbours apparently tolerant of the Cuban music pumping out of her small flat. She is an accomplished flamenco dancer, which must make living downstairs a tad fraught. Unmarried and "permanently in love with someone although that person changes all the time", she claims to be, and seems, "very happy, which is the main thing. I'm a very happy person."

The career-path of a young actress is full of difficult choices, some of them dead-ends – couldn't she just tap a few of her mother's contacts? After all, Geraldine has been in the business for nearly 50 years now, and the Chaplin name must open doors – even if only to the curious. "Ironically, I don't have many contacts," she says. "My mother doesn't have much of a social life with other A-list people. Which in a way I'm very grateful for, because if I do make something of my career I will be able to say it wasn't because I was a Chaplin. Or maybe it will still be because I'm a Chaplin – I will never know that."

Does that fact torment her? "No, it just puts a healthy amount of pressure on me – a reminder of what one can do with one's life if one works hard, at the same time these are very different times." And then she puts on a mock Lady Bracknell accent. "Nepotism doesn't really get you anywhere any more, which is a terrible shame."

'The Hour' begins on BBC2 in late July

Charlie's clan: The other Chaplins

Geraldine Chaplin

Daughter of Charlie with his fourth wife Oona O'Neill. She studied ballet before being discovered by David Lean and cast in Doctor Zhivago (1965). She has had a prolific career as an actress, even playing her own grandmother, Hannah, in a film about the life of Charlie Chaplin.

Sydney Chaplin

Third son of Charlie, by second wife Lita Grey. Sydney turned his hand to stage acting, winning a Tony Award in 1957 in Bells Are Ringing and starring opposite Barbra Streisand in Funny Girl in 1968.

James Thiérrée

Son of Jean-Baptiste Thiérrée and Victoria Chaplin, Charlie's third child with O'Neill. James appeared in his parents' circus shows as a child before staging his own vaudeville performances at venues around the world.

Kiera Chaplin

Daughter of Eugene Chaplin, the British actress and model has appeared in Vogue, Elle and Vanity Fair, and was voted one of the world's most eligible women by FHM US.

Carmen Chaplin

The daughter of Michael Chaplin, Charlie's second child with Oona. Continuing the family tradition, Carmen, who lives in New York, has acted in films including My Favourite Season, All About the Benjamins and The Serpent's Kiss.

Holly Williams