Brenda Blethyn turns TV detective in Vera

"She's kind of like an ordinary person really. If you sat next to her on the bus and struck up a conversation you'd probably be talking about the two-for-one prices down at the Co-op." Two-times Oscar-nominated actress Brenda Blethyn OBE is describing her title character in a new ITV detective drama, Vera, but she might as well be talking about herself. Down-to-earth, giggly, slightly apologetic and given to unexpected outbursts – including "I got married last year – after 35 years together", but more of that later – there's nothing ordinary about the way that Blethyn has risen like cream, almost imperceptibly, to the top.

We meet in a "media lounge" at ITV's London offices, a womb-like room with plum-coloured wallpaper, expensive leather sofas, and a sideboard containing the inevitable hospitality fruit-bowl and bottled mineral water. It might equally be an upscale psychotherapist's consulting room – although an actor less in need of therapy it is difficult to imagine. "I hope my breath doesn't smell of garlic," she mutters in her mildly chaotic way, before mentioning that she skipped breakfast this morning. I'm left to wonder about her dietary habits.

Vera, in which she plays DCI Vera Stanhope, Geordie murder-detective heroine of Ann Cleeves' novels, marks something of a departure for an actress better known for portraying mothers – whether James McAvoy's in Atonement or Keira Knightley's mother, Mrs Bennett, in Pride & Prejudice. "I haven't played anybody in the police force before, except in a training film about 30 years ago teaching children not to go with strangers," she says. "Ann Cleeves' character is much bigger physically than I am. She's shambolic, she looks like a bag lady... like Columbo, but even more so – she's always scratching... It makes you wonder, 'Who should we get for this part? Brenda Blethyn...'."

Blethyn turned 65 in February, way too old for the police force even in these work-till-you-drop times, so it's just as well she looks a lot younger ("I never have looked my age – none of us in my family do"), although her voice sounds older. It has that slightly weak, rather plaintive timbre made famous in Mike Leigh's 1996 movie Secrets & Lies – a film memorably described by biographer David Thomson as "a raw slice of life or an over-juiced piece of shtick – it all depends on your response to Leigh". Blethyn played Cynthia, the "downwardly immobile" white working-class birth mother traced by her upwardly-mobile black optometrist daughter Marianne Jean-Baptiste, and in real life she sounds just like Cynthia – minus Cynthia's trademark "Sweetheart", or rather "Sweetheaaaart". I'm suddenly tempted to blurt it out, but decide it's still too early in the interview for such frippery. I needn't have worried, because Blethyn isn't in the business of taking herself all that seriously. There's no pomposity to prick here.

By her own estimation – an estimation that tends to downgrade her own talent and determination – Mike Leigh was the making of Blethyn. She made her television debut in Leigh's 1980 drama Grown-Ups, while Leigh's Secrets & Lies turned her into an international film star. "I learnt so much from him... I've got so much to thank him for," she says. "Before I worked for him I was kind of lazy – not lazy, I'm a hard worker, but I didn't know you had to know what the character's surname is if it's not in the script. Of course you should know that – it's knowing everything there is to know about the character, whether it's apparent or not in the filming of it. For me it adds another dimension to what you're doing. And for that I thank him from the bottom of my heart."

Blethyn was at the National Theatre when she first encountered Leigh, but not as a fresh-faced Rada graduate or anything like that. Her journey to the London stage came the long way round, via a failed marriage and 10 years as a clerk for British Rail. Blethyn has no thespian forebears, except a father who couldn't tell a story without play-acting the part, and rather alarmingly she suddenly jumps up from her chair at this point and imitates her dad in action – a performance in which he seems to be playing Long John Silver.

Born in 1946 with the splendidly Dickensian name Brenda Bottle in the splendidly Dickensian Kent port of Ramsgate (Bleak House is just along the coast), Blethyn's father, Mr Bottle, was a chauffeur for a family in nearby genteel Broadstairs when he met his mother, a maid in service in the same household. He was working as a mechanic by the time Brenda, the youngest of nine children, came along. "My dad was born in 1894 and lived in Kent all that while, and he had this accent that was olde worlde," says Blethyn. "When I went down I never went straight in the house, I'd knock on the door and he'd say 'Oh crikey, if it ain't our Brenda, wow, loo' if it ain't a red-letter day'.

"It was kind of a Victorian upbringing, because they were Victorians, you know. We had sod all, but you'd have thought we had the crown jewels the way they carried on. We were squashed in – the boys had one room, mum and dad had the other room and I was in the parlour." And what of the story I had read that they sometimes went without shoes? "Oh, no," she laughs. "We always had shoes on, although to earn some money when I was a teenager I would mend shoes –I had learnt how to do it because we had to mend our own shoes. Everyone was in the same boat back then, but there was an air of optimism it seemed, things were only going to get better, so you didn't feel deprived. All I can remember is laughing."

Laughing all the way to British Rail. By the time she was 19, Blethyn was working as a shorthand typist at the nationalised company, and it was here that she first caught the acting bug – playing in BR's amateur theatrical troupe – and met and married the man whose surname she still carries to this day, Alan Blethyn. Her decision to apply for drama school coincided with the collapse, in 1973, of that marriage. "Between being accepted at drama school and actually starting in September, my marriage... My husband fell in love with somebody else."

She says he's "a lovely man... I hardly ever see them but I still have affection for him, absolutely. Lovely man. And her..." she says, referring to the woman he left her for, which seems almost saintly. "Yes, well, what's the point? I was ever so upset at the time, but I've grown up since then." And it's at this point that she blurts out, perhaps to prove that the story has a happy ending, that "I got married last year, after 35 years" – a nice little scoop, because in all the newspaper cuttings, Blethyn is famously unmarried to her long-term partner, Michael Mayhew, who used to design posters and programmes for the National Theatre.

"It wasn't exactly a proposal," she laughs. "Well it was a proposal, but it just drifted into the conversation... on Skype. I was in Northumberland working on the pilot of Vera and I thought, 'Blimey, if he could see me now... Hold on, he can see me!'. I said 'You could at least go on one knee' – and he did and disappeared off the screen!"

She fishes her iPhone out of her handbag at this point to show me a picture of their wedding day at Peckham register office, but can't get it to work. Their honeymoon – "silly to say that at our age" – was supposed to involve Michael joining her for Christmas in New York, where Blethyn was doing an off-Broadway play, but the snow chaos that closed Heathrow put paid to that.

She and Michael have never had children, despite having "hundreds" of nieces and nephews, and even a great-niece. "There's no answer to it really, or I might just be selfish," she says. "I often sit and wonder 'What if?' and then I think of all the things I've got instead. I don't seem to have been brave enough to have made the decision to have a child. If it happened accidentally I think it would have been a different matter. Unplanned it would be different. Some people combine the two – I suspect I would have been devoted to the children."

But back to her first marriage, or rather its aftermath, which Blethyn spent at drama school in Guildford before getting a job with her agent answering the phones. "A job came in and he'd named all these women and I was pointing at myself and he went 'No, no, no'. 'Let them say I'm not right, not you,' I said, and so he put a call through and I got an audition and by the time I got back to the office I'd got the job."

That job quickly led to five years at the National Theatre where she played Cordelia in King Lear, Joan of Arc in the King Henry cycle, as well as TV work opposite Simon Callow in the sitcom Chance in a Million. Her movie debut was in Nicolas Roeg's The Witches (1990); next came Robert Redford's Oscar-winning A River Runs Through It (1992), playing Brad Pitt's mother – her first major mother role – before she was Oscar-nominated for Secrets & Lies. That led to nine years of solid movie-making, including another Oscar-nominated mother – this time Jane Horrocks' in Little Voice. Not that the prospect of an Academy Award unduly impresses her.

"It's like someone saying, 'Would you like a cup of tea?'," she says. "'Oscar-nominated', it's terribly flattering, but really it's only an award created by the film industry for the film industry... It's only those films that have an enormous machinery of distributors behind it. Everyone got to see The King's Speech because of Harvey Weinstein. But forgetting all that – it was very flattering. My family were beside themselves. My brother rang me up and said, 'I'm so proud of you, you're so fantastic' and I said, 'But I didn't win' and he said, 'It doesn't matter, we're so proud of you, you're so fantastic...'."

Hollywood now knew who Brenda Blethyn was, but films didn't exactly fall into her lap after Secrets & Lies, and once that movie and its promotion had finished, Blethyn stayed on in LA for some self-financed hustling. "My agent said I should stay there and meet all these agents, but I'd have to pay for myself – it would be an investment. I was on a very tight budget. I remember I couldn't afford room service so I went and bought myself some cereal and a bottle of milk, but there was no cutlery in the room so I found a vase and a shoehorn... I thought 'I've arrived'." The anecdote summarises Blethyn, really – the totally un-starry attitude, the ability to "make do" and the humorously self-deprecating pay-off line.

She's considerably more comfortably off now, although not film-star rich, with houses in south London and Ramsgate ("but now I'm on the West Cliff – which, when we were growing up on the East Cliff, was always considered to be posher"). She's hoping that Vera becomes a successful, long-running show, so that she can spend six months of the year filming up in Northumberland and the other six months pottering – "doing all the things I've been putting off because I've been away so much: painting the window panes and buying some furniture that goes together, instead of making do with bits and pieces all the time. God, I sounded just like my dad then..."

Stopping acting isn't on the cards, although she once did prematurely announce her retirement to a journalist. "And I was inundated with job offers, one of which was Pride & Prejudice, so I was well pleased." She was awarded an OBE in 2003. Does she think she'll soon be similarly ennobled as Dame Helen Mirren and Dame Judi Dench? "I can't see it happening," she says, beginning a short conversation with herself. "It would be nice, but why would it be nice? It's quite nice as it is now... Yes, it would be nice, but it's not going to happen. I'm way at the back of the queue." Nice is a word that peppers her vocabulary.

At the end of my allotted time with Blethyn, she finally manages to warm up her iPhone and find the picture of her wedding day, with Michael in the garden of Peckham register office. "We had a pub lunch. Just two witnesses. And it was lovely." She's right – Dame Brenda would never do. She's nice as she is – plain, ordinary Brenda Blethyn. Or is it Brenda Mayhew now? I forgot to ask. Either way, she's very nice.

'Vera' begins on ITV1 on Sunday 1 May