The housemaid's tale: Joanne Froggatt rips off her pinny and sets her sights on Hollywood

To quo vadis restaurant on Dean Street – a Soho institution since 1926, apparently, so that would be the silent 1925 movie version of Quo Vadis? it's named after, and not the 1951 widescreen epic that dropped the question mark from the title. I must have walked past its neon sign at least one hundred times, and each time I thought the same thing: how camp it sounds! The decadence of Ancient Rome right in the heart of London's theatreland, so that it was something of a thrill to pay my first visit – not to eat the food (much improved, by all accounts, now it's being cooked by Jeremy Lee), but to take the lift up to its private member's club and have coffee with Joanne Froggatt, the actress better known to 10 million Sunday night TV viewers as Downton Abbey's head housemaid Anna Bates.

Anna is married to convicted ex-wife-murdering valet John Bates, although he didn't do it, of course – unless of course he did do it, in which case Julian Fellowes is a far more twisted writer than I had thought. Whether or not Anna and John are to be reunited remains to be seen – partly because, as Froggatt says, "I haven't seen the scripts yet... we started filming the new series just two days ago and we don't really feature until later on," and partly because she wouldn't tell even if she did know. "I'm not sure how much I should say," is a constant worry for her when discussing future projects. There are no plot-spoilers in this interview.

Anyway, there's a piquant irony in meeting a star of Downton Abbey at Quo Vadis – for, as it states on a blue plaque on the restaurant's exterior, Karl Marx and his family lived in two rooms on this premises between 1851 and 1856. This luxury dining establishment was then a "hovel" (Marx's words), in which he wrote much of Das Kapital and, tragically, lost three of his children. There is precious little evidence of revolutionary ferment at Downton, although the new series, set at the start of the Roaring Twenties, is heading towards the General Strike of 1926. Froggatt, however, has had her head turned by more material considerations. "I have a new uniform," she would have trilled if she was the trilling type. Instead she has an evenly modulated and attractively soft Yorkshire accent. "It's very exciting compared to the dresses I've worn in the last two series. I've got one of Lady Edith's skirts and one of Lady Mary's dresses."

Marx may have wondered why Anna didn't just appropriate Lady Mary's entire wardrobe, but then it's doubtful whether Downton would have been the German thinker's cup of tea in the first place. Contemporary historians certainly don't like the show, especially the anachronistic fraternising between masters and servants, while Simon Schama has urged American viewers to abandon this "servile soap opera" and "silvered tureen of snobbery". America rewarded it with Emmys and adulation.

"And it's the top show in Spain," says Froggatt, still not trilling. "In Australia it's second top... it's just incredible." In fact, Downton serves its silvered tureen of snobbery to well over 100 different territories, where it is gobbled up by grateful huddled masses. How early on did Froggatt realise that she was part of something special? "I think when we started filming we all knew that it was something really, really good," she says, "but we never dared imagine it would have hit the dizzy heights that it has."

Not that Froggatt strikes me as the type to get dizzy. She hasn't yet clapped eyes on Shirley MacLaine, Downton's latest new recruit, who is joining as Lady Cora's mother, Martha, although she is chummy with the actress who will be MacLaine's sparring partner in the third series, Dame Maggie Smith. "I saw her today," she says. "She gave me a big kiss." Froggatt's best friend on set is Michelle Dockery, who plays Lady Mary, although she adds – with an unfortunate turn of phrase (perhaps she does harbour subconscious revolutionary leanings after all) – "the whole cast gets on like a house on fire".

But enough about Downton Abbey, especially as this interview opportunity comes courtesy of the BBC, who must still be kicking themselves for not getting in there first with their rival tureen of snobbery, Upstairs Downstairs. Froggatt has been making a new drama for the broadcaster, True Love, five overlapping tales of passion in which she plays David Tennant's wife. Vicky McClure from This is England plays a former girlfriend of Tennant's character, who suddenly comes back into his life, creating the sort of situation that Adele fantasises about in "Someone like You".

True Love has been directed by Dominic Savage, who belongs to the Mike Leigh school of improvised drama. "Scary, but I really, really enjoyed it," says Froggatt. "As an actor, or as a person, I like to do things that are challenging." The whey-faced, waif-like 32-year-old thanks me good-humouredly for saying that I can see something of Joely Richardson about her profile, although you can tell she's not the sort to let compliments go to her head. In fact, Froggatt seems to have a very sure sense of herself, that perhaps helps explain why she is regularly 'discovered' every four years or so, as if she has just popped up from nowhere. Looking younger than her years probably helps with that impression. I was amused, I tell her, to see that she was recently awarded Best Newcomer at the British Independent Film Awards, for In our Name, in which she plays a soldier suffering from post-traumatic stress disorder, whereas "I've been around quite a long time," she says, finishing my sentence with a wry chuckle. "I know... Well, I am a newcomer in film ... It was really special to get that award because it was so low budget."

The first time that Froggatt was discovered – apart from her stint as Coronation Street's teenage mother Zoe Tattersall (we'll come to that) – was in 2003, when she was nominated for a Royal Television Society Award for her leading role in the true story Danielle Cable: Eyewitness, in which she plays the eponymous fiancée of Stephen Cameron, the 21-year-old stabbed to death in 1996 by convicted criminal Kenneth Noye on the M25 in Kent.

Cable, then aged 17, was praised by police for her courageous courtroom evidence which was crucial in convicting Noye for murder – and was duly placed on the witness protection programme. Froggatt was taken to meet her. "The producers sent a car for me," she says. "I didn't know where I was going, so we met in a hotel reception somewhere in the country with her and her mum and a police escort – plain clothes, obviously – and we chatted for a couple of hours. We were a very similar age so I could relate to how difficult it must have been to be taken away and to go through such a horrific ordeal... being removed from your family and friends and support systems."

Froggatt was next discovered when she played Maureen Smith, the sister of 'Moors Murderer' Myra Hindley, in the 2006 film, See No Evil: The Moors Murders, in which Froggatt's good friend Maxine Peake played Hindley, and then again the following year in Murder in the Outback. Once again she was playing a real person, Joanne Lees – the British girlfriend of murdered back-packer Peter Falconio, whose body has never been found. Despite DNA evidence that convicted Australian drug runner Bradley Murdoch of Falconio's murder, Lees had to endure a trial-by-media after she gave a seemingly unemotional TV interview with Martin Bashir.

"The producer sent me the unedited version of the interview she did with Martin Bashir," says Froggatt. "The edited version was deemed incriminating. The thing is she just wasn't an openly emotional person, but that doesn't mean that she was involved in murder. It was interesting to see because there's one point where he asks about Peter and she gets really upset and it takes her about five minutes to pull herself together, but on the edited version he asks her, and she flicks her hair and it carries on to another question."

In between being regularly re-discovered, Froggatt played John Simm's mother in the time-travel cop show Life on Mars, Antony Royle's girlfriend, Saskia, in The Royle Family ("I don't think I've ever laughed so much on set"), and a number of mortgage-paying parts in ensemble drama series such as Red Cap, Moving On and The Street. "I try to do things that are different and diverse and really interest me," she says. Froggatt has certainly shown a singular determination since, as a 13-year-old living on a farm in North Yorkshire, she packed her bags and headed off to stage school at the other end of the country.

Her parents ran a corner shop until they decided to follow their dream of self-sufficiency, starting a rare-breed sheep farm on a smallholding near Whitby. "They had a flock of, I think, 120 sheep at the height, so my dad used to milk the sheep and my mum used to make cheese and yogurt out of the sheep's milk – so that was their business," she says. "The way they've brought my brother and I up is just to have a go at everything. They gave us this attitude that you've only got one life and you really must make the most of it."

Her secondary school headmaster got her interested in acting, Froggatt joining a drama group in Scarborough. "I just loved everything about it," she says. "I got to hear about The Stage newspaper, so I started getting that every week, and all the adverts were for dancers on a cruise ship and that sort of thing... things I was far too young for. But also I saw adverts for stage schools in there and I thought 'That's what I want to do'. So I went to my parents and said I want to go to stage school and they went, 'Right... OK... you find out about it and we'll take it from there', all along hoping I'd lose interest... it'd just fizzle out."

Of course it didn't fizzle out. Froggatt doesn't trill or get dizzy and she certainly isn't a fizzler. "It took about 18 months because I had to apply to the council for a grant, but there were no grants for people my age... so eventually through lots of letters we managed to get a foot in the door, and I auditioned for the council and they basically made a grant for me." Which is how she found herself at Redroofs Theatre School in Maidenhead, Berkshire, and then, by a circuitous route, to the nation's favourite soap, playing Coronation Street's teenage mum, Zoe Tattersall. "It was supposed to be for a few episodes and it lasted 18 months," she says. "My baby died of meningitis – I was written out – so it was not my decision to leave.

"At first it was very, very hard to break away from that in terms of being taken seriously as an actor and having longevity. At the time I left, which was 10 or 12 years ago, there was still a lot of snobbery in the industry about being in a soap opera, which was frustrating because I was still a child really. I was 'You can't write me off yet... I'm only 18... give me the chance to prove what I can do'."

And that is what duly came to pass, although there is obviously much more chancing and proving in the pipeline from this quietly determined young actor. She has just finished filming an adaptation of Irvine Welsh's Filth, with James McAvoy and Jamie Bell, and uwantme2killhim?, a psychological thriller based on a true story about two teenage boys who strike up a lethal online friendship. And later this year, Froggatt, who lives in High Wycombe, will be marrying her fiancé, James, who owns an IT company. "He's a fan of film and theatre," she says, which is lucky, because it might have been tricky if James was only really taken with spread-sheets and operating systems. "He's really calm about a lot of things and keeps me on an even keel," she adds, although it's hard to imagine her on an uneven keel.

What Froggatt really wants to do now is to make films, an ambition that's become a lot more realistic since the international success of Downton Abbey. "I've got a new manager [in Hollywood] and I'd love to work out there ... Hopefully there's something a bit different about me. I'm not a classically beautiful face... I always play girls who are quite traumatised, or a plain girl, but I'm happy with that. I've played some really interesting characters – I've loved doing them – so going out there I couldn't compete with Julia Roberts." It sounds like a game plan to me, I say – and one that should secure greater longevity than competing with Julia Roberts. "It's not the be-all-and-end-all... I wouldn't want to move out there permanently and just sit around doing nothing," she says. "I'd probably want to go out there for a few months which is probably what I'll do at the end of this year. But one day... maybe..."

We part – Froggatt to have her photograph taken, me to exit by way of Quo Vadis's reception, where a well-dressed woman in her late fifties is screaming abuse into her mobile phone, tearing a strip off an underling in a way that suggests that the receptionist might as well not exist. I can't help feeling that this is what would really happen in a real place like Downton Abbey – the servants completely invisible to the masters. Or perhaps that was just the spirit of Karl Marx communicating itself.

'True Love' starts on BBC1 in June