`Does nobody ever believe anything I do?` asks Dame Judi Dench

In a small room in a large hotel in London, a woman often described as our greatest national treasure – the actress who once beat the Queen into second place as Britain's most liked and respected person – is sounding off about modern life. She isn't holding back. As she has grown older, Dame Judi Dench told the Guardian, grey eyes sparkling with laughter, she has become more and more angry.

"I hear myself saying things that I know old people say. Like when I want to ring up about something," her voice lowers dramatically, "and I get that f***ing recorded message which tells me to press one, two, three or four, and then you press four and there are two more recorded messages and YOU CANNOT TALK TO ANYBODY! It makes me absolutely mad." What happens when she finally gets through and the operator realises to whom they're speaking? "I don't give them a chance to comment. I just give them an absolute mouthful and ring off." She chuckles.

Dench is not at all what I expected. On the one hand, I am used to reading that she is saintly, sweet and suburban. This is clearly not the case. She wears her anger with twinkling pride. On the other, based on her recent parts – including a pair of queens, Lady Bracknell and a borderline psychopath – I was imagining someone grand, slightly terrifying.

That last expectation increased after seeing her latest film, Rage, a strange, experimental project that features 14 actors playing fictional figures in and around the fashion world, who give monologues before a plain backdrop. There's Jude Law as a self-absorbed model; Eddie Izzard as a slick mogul; then, as fashion critic Mona Carvell, Dench looms on screen, her mouth a bloody slash, eye sockets lined with kohl. Carvell is a skull of a woman, much given to haughty pronouncements: "Fashion is not an art form – if it's anything at all, it's pornography." She is tough, steel-eyed, sour.

The woman who plays her is none of these. Well, tough, possibly. But rather than seeming grand or intimidating, Dench is actressy in the best way: spirited, playful, her ring-heavy hands gesturing expressively, touching wood, miming a memory. I ask what she thinks of Rage, and she says she hasn't seen it, and motions to the poster, "I'm reading the cast list for the first time now!" She was attracted to working with British arthouse director Sally Potter, and the fact that it was unlike anything she'd done before. "I like to do something that's not expected, or predictable. I had to learn to smoke a joint, and I set my trousers alight. I've never been good with cigarettes."

Rage is the latest twist in a surprising late film career. Dench is 74, and just over a decade ago – at an age when most actresses are bemoaning the lost limelight – she began a path to six Oscar nominations. "It's all very surprising," she says, "because it came so accidentally. It came because Harvey [Weinstein, the producer] saw Mrs Brown, which had been made for television, and said it should be a film." Weinstein's company, Miramax, went on to distribute Iris, Chocolat and Mrs Henderson Presents; Dench has joked that, "Harvey's name [is] tattooed on my bum."

Her film career seems even more unlikely when you consider that, as a young actress, Dench was told that she had "everything wrong" with her face. She doesn't seem to have been bothered. "I didn't think I'd have a film career at all, but theatre's what I love most, anyway. If you'd said to me 49 years ago that I'd come to enjoy the process of filming, I wouldn't have believed you."

Dench's love of acting stretches back to childhood, and a junior school performance as a snail. She grew up with a GP father, Reginald – official doctor to the Theatre Royal, York – a passionate Irish mother, Olave, and two older brothers. The family were keen amateur actors; in the 50s, father, mother and a teenage Judi appeared in the York mystery plays. By this time, Dench had abandoned her plan to be a ballerina – "My Dad said, 'You do know that if you're a dancer, you will probably have to give up when you're about 40'" – and after a brief dalliance with theatre design, she followed her brother Jeffery to study acting at the Central School of Speech and Drama in London.

She left with a first-class degree, then pitched headlong into a high-profile role as Ophelia opposite John Neville as Hamlet at the Old Vic. Expectations were high; the reviews were bad. "She trips over her own publicity and falls flat on her pretty face," wrote one critic. Dench found the attention difficult. "Kenneth Tynan gave me a very good notice, and so did Milton Shulman, so I clung to those two like a man with a piece of straw. It was very hard, but maybe it's good when you get a hammering so soon."

She seems to have been fuelled by insecurity ever since. Has she had any period out of work, I ask, and she slams her glass on the table and grasps the wood for luck. Should I not even have asked? She shakes her head, tight-lipped, eyes darting nervously. "I'm not going to answer!" she says finally. "I've always been very, very insecure about where the next job is coming from."

But surely she can rest on her laurels? "No," she says quickly. Is she a workaholic? "Yes," comes even quicker. She has just filmed the musical Nine, and says that when she was cast, "I was absolutely overcome. I don't take any of it for granted, ever."

It often seems Dench has spent her life trying to recreate the theatrical family that surrounded her as a child. Her happiest times are in a company, and she sticks up vociferously for workmates. With Cranford, she felt the crew were "worked to the utmost limit to get it done. And they did it beautifully. I wrote to Mark Thompson [director general of the BBC] and said that it's impossible to do that amount of work in less time than that. I also mentioned that intensely irritating thing, that the moment a programme is over, the cast list flashes by, then the credits are moved to the side of the screen and you can't see the crew. Well, I heard subsequently that they said, 'Oh, only people's mothers complain about that.' But in actual fact a lot of people complain about it. I quite like when I've seen a thing to know who's best boy and who's the gaffer. I still don't know who directed Bleak House. It's people's careers, and somebody watching it might think, 'God, that's beautifully done.' Well, good luck if they want to find out who did it."

As a young actress, Dench loved being in rep, where you could "make mistakes, and have a go at playing some terribly old person when you were 23. Ideally, what I'd like is to be in a company and not be doing the same play every night." She harks back to Stratford in the 70s, when she "was doing Macbeth, and Comedy Of Errors, and Much Ado, and King Lear. I was asked once, 'But when you're playing Lady Macbeth, that must take over your entire day?' And I said, 'Well, it can't because in the evening I've got to play Beatrice in Much Ado. So it's a quick slough off at tea time.'"

It was around this time that her status as a national treasure began to build, and over the years this has inspired some quotes that, even if jokey, are nauseating. Stephen Fry said, "Railings should be built around [Dench] so that all may admire her in an orderly and respectful fashion"; Kate Winslet said she "would work with Judi if I had to be a tea lady hovering in the back of frame"; and Ian McKellen was moved to suggest that "one of the great joys of being alive in England in the 21st century is being around when Judi Dench is".

McKellen starred with Dench in Macbeth, and has implied that, whatever role she plays, the audience fall in love with her. "Crap!" she says. "Crap. He's talking through a hole in his arse." I ask how she feels about being designated a national treasure, and she makes a face. "I don't like that very much, I'm afraid. That sounds pretty dusty to me. It's Alan Bennett and I behind glass in some forgotten old cupboard. I don't like it at all."

Is there any role that could banish that reputation? She points to Barbara Covett, her character in Notes On A Scandal, a creepy, conniving, deluded woman. "I think that gave it a bit of a boot." She was upset a few months back when the British Board of Film Classification published its annual report, which said that every film she swears in prompts complaints from the public. "That upset me terribly, because I thought, in a way, that cancelled out the last 52 years. I thought 'Does nobody ever believe anything I do? Can't they for a minute think that I am playing another person, in another world, with another personality? Must they write and complain that it came out of my mouth?' I was very depressed about it."

Dench's reputation does seem strange – after all, contemporaries such as Maggie Smith and Vanessa Redgrave don't inspire the same expectations of sweetness. And it's not as though she has shied away from risk. In the 70s, she starred in the BBC play, Langrishe Go Down, in which she had to appear nude. "Well, I was allowed to wear espadrilles and a wig and earrings. And I had the most wonderful dresser called Lizzie. I was terribly nervous, and I had to run across a meadow to this bush, where Lizzie was hiding, and she said, 'Judi, you look like a lovely birthday card!'"

She thinks her saintly reputation may stem from the fact that she has appeared "in situation comedies, so I'm in people's sitting rooms a lot", and it probably is the breadth of her career that inspires such wide-reaching devotion. For lovers of high art, there are her Shakespearean roles. For musicals fans, there are performances in A Little Night Music, and as Sally Bowles in the first London production of Cabaret (Hal Prince, who directed her, considered Dench "the most effective of all the people who played the part"). Those who like costume drama are rewarded with Cranford; those who like sitcom get A Fine Romance and As Time Goes By. There are the credible films, such as Notes On A Scandal, and less credible ones, such as The Chronicles Of Riddick. Then there are the Bond films. Did she enjoy coming in as Bond's boss, M, to break up the boys' club of those films? "You bet. Give them a bit of a ticking off, yes." Is she a feminist? "No, I wouldn't call myself a feminist at all, really. I don't know what a feminist is. I believe in women having a say."

Is she political in other ways? She says she's "very, very angry about Iraq. And I'm very angry that we seem to be in such a mess and [all the politicians] take 16 weeks' holiday. That makes me despair." Does she think the country would be in better shape if the Tories came in? "No," she says, "I just think that it would be better if… I don't know. I just remember dancing in the streets when Labour got in." She once went on a Ban The Bomb march with Vanessa Redgrave: "I think Van was arrested, but she had a matinee," so they let her off. Redgrave was a contemporary of Dench's at drama school, and once wrote they were all envious of her natural ease. I put this to Dench, and she shrieks. "We were all very envious of Vanessa! At drama school, they would say, 'Now, it's prologues', and all of us were completely, totally inept, except Vanessa." Are they still friends? "Yes! Yes we are."

She is great friends with Maggie Smith, too – she has always been surrounded by actors, even away from the stage. Her brother Jeffery still acts, as does her daughter, Finty Williams, who has just been cast in a production of Bedroom Farce, directed by Sir Peter Hall. But the shadow of Dench's success hasn't always been easy for others: Finty has talked of times when she thought, "I'm never going to live up to this woman's image." And Geoffrey Palmer has said of the actor Michael Williams, to whom Dench was happily married for 30 years, that "the fact that all his married life he was Mr Judi Dench, that's difficult for any man".

Michael died of cancer in 2001, and Dench says she hopes her success wasn't a problem for him. "It shouldn't have been, because he was such a good actor, and has done such marvellous things. I think it's only if other people's attitude towards you is rather selective" – if they single you out – "and you're with your family. I don't like that. It's bad manners on other people's parts."

She has always liked to live with extended family, and her daughter still comes to stay during the week; they share the house with five cats, a dog and two fish, "one of which I saved from drowning by giving him the kiss of life". He used to be called Rhubarb. Now he's called Lazarus.

Terry Hands, a director at the RSC in the 70s, once said that "at least half the company was in love with [Dench]. She was a pin-up for many young men." Does she still get a lot of propositions? "No! No, you don't get any propositions when you're rising 75." She laughs. "I have a lot of very, very good friends." There is a long pause, and I ask if she's lonely. "Sometimes I get quite lonely, yes. Well, I'm not good at my own company. So, um, of course it would be." She stops briefly, and thinks, her eyes misting up. Then she gets firm with herself. "Oh no, I'm not even going to go there. But, um, yes…" There is another long pause. "Anybody who's had a very happy marriage must feel the same. On the one side, you feel fantastically lucky you had what we had – we knew each other 39 years and were married for 30. And yet, when the person is not there, you suddenly think, oof, it's not wonderful." She pauses, then spits out her next words. "That's rather a stupid reply." Not at all. She looks wrung out. "It is."

Still, work makes her happy, and she has no plans for retirement – the idea is anathema. Does she get a kick out of every new job? "I certainly do. I've never got through a job without suddenly having a problem come up in front of me that I have no idea how to tackle." Is that what keeps her going? "Yes, I like that. I love it."

Rage premieres on mobile phones on 21 September and in cinemas on 24 September. For details, go to ragethemovie.com

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