In the last couple of years, though, more or less coinciding with her 50th birthday, people have been reverting to the old name, perhaps intuiting, along with its owner, that "Frankie is a very young name: I feel rather odd being called Frankie at 50. The last two jobs I've done, everyone called me Frances. Occasionally I said, 'Call me Frankie if you like', and they said, 'Uh huh?' " She says the "uh huh?" with the withering sarcasm that the young reserve for the middle-aged trying to stay hip and spry.
There's a tempting neatness in this unbidden change. Since people started to call her Frances, a career that has never assumed a conventional shape has started to look less amorphous and random. "I'd like it to have happened at 41 and not 51, but then I think 51 now is like 41 was in the 1950s. I think we're all allowed to go on a bit. I'm not sad any more, or bitter that I didn't do what I didn't do. I do feel optimistic."
It's scarcely a tale of blockage and failure, but there is a sense in which opportunities have been repeatedly lost, wrong turnings taken, strange connections made. She was in Peter Brook's Dream, the most famous experimental production since the war, in which she gave us the first of her many gawky, vulnerable, sexually frustrated women. And yet she's hardly done any Shakespearean comedy since. Then there was Rising Damp, which earned her unheeded fame in millions of households containing not a single theatre-goer. But she took 20 years to do another sitcom (Every Silver Lining, a stinker). "When people talk about Rising Damp," she says, "I have to take a beat, because it was a tiny part of my life. Thank goodness it was a good one - if you're going to be in one, be in a good one. But it has nothing to do with the rest of my life."
Mostly thanks to Rising Damp, where she learnt comedy at the feet of Leonard Rossiter ("a genius"), she is one of this country's most famous actresses. And yet she has somehow hovered in the shadow of others. Three Tall Women was Maggie Smith's triumph; but Frances de la Tour, as her daughter, was brilliant too. In When She Danced, her friend and fellow socialist worker Vanessa Redgrave was incandescent as Isadora Duncan. But Frances de la Tour, as her spinsterish secretary, was wonderful too. She was warned at drama school that "you're not typical and you may have to wait a very long time before you get the success we think you deserve". From the start she looked interesting, quirky and, in less broad-minded times, unstarry. With French blood on her father's side (a De la Tour escaped the Revolution) mixing with a dominant Macedonian gene from her mother's, she was never going to qualify as prettily English - "chocolate boxy," as she calls it. "I was lanky and tall and just different. If I was 20 now I would have had a different career. I could have played anything." She agrees that she might have taken the sort of trajectory followed by Juliet Stevenson, another actress with a rich, deep, creamy voice and charismatic, unclassical features.
So, everywhere you look, there are odd little ironies in her career. During six years at the RSC she hardly ever took any of Shakespeare's great parts for women. In As You Like It she was never Rosalind, whom she was born to play, but Audrey, the slovenly bucolic dolt. "I was a walking, talking, living Rosalind," she says. "I went to Oxford to play it because the RSC wouldn't give it to me. Madness really." She left the company not long after playing a heap of rags that Paul Scofield had to step over. A few years later she wrote to Trevor Nunn to ask why the grand roles had never come her way, and framed the reply. "I still don't understand it. 'Dear Frankie, I'm thinking about your past, present and future. Love as ever, Trevor.' I thought, what? What on earth does that mean?"
And then there was Chekhov. With her looks she'd pass for a Russian, but when she starred (again opposite Redgrave) in Chekhov's Women, she had never actually played any of Chekhov's women. When she took the show to Russia in 1990, "all the directors and actors I met just couldn't understand it." In the early 1980s her then husband Tom Kempinski wrote Duet for One for her, she snaffled up every award on offer, but the Broadway transfer went ahead without her, and in the dreadful film version the role of the wheelchair-bound cellist went to Julie Andrews. "At the time it was very upsetting."
"I think she's handicapped by her individuality," says Sean Mathias, who directed her in Cocteau's Les Parents Terribles (and has never called her Frankie). "For me she is absolutely up there with Maggie Smith. It's an indictment of our lack of imagination in this country that we have to pigeonhole people." It can't be a coincidence that, despite not really enjoying the artistic loneliness, she's done several one-woman shows, including one in Japan.
But her fifties find the script in the throes of revision. She spent some of her childhood in Cookham, where she met (but was not especially interested in) Stanley Spencer, so when the National asked her to play either of his wives opposite Antony Sher, it would have been biographically tidy to say yes. But she didn't. "It wasn't quite enough for me to do considering what I had just done. It was time I did something more stretching." So in September she opens at the National in Blinded by the Sun, a new play by Stephen Poliakoff. Though she isn't allowed to say where or when, soon she will finally get to play Ranyevskaya in The Cherry Orchard (at the third attempt: she turned down 52 weeks of it in Stratford and another effort to do the play with a Russian director, composer and designer never came off). She's also lining up her Cleopatra ("an amazing, cultured woman"). The timing of all this depends on whether or not she gets to play Maria Callas in Terence McNally's Masterclass, currently on Broadway. "That is not definite because the American producers have to agree to me doing it and they haven't yet." But first off, in Cold Lazarus - Dennis Potter's sci-fi sequel to Karaoke - she has landed her biggest and best television role in 20 years.
Lazarus was one of those two jobs in which Frankie went back to being called Frances. She plays Professor Emma Porlock. Ever since "a person on business from Porlock" knocked on Coleridge's door while he transcribed the dream-inspired "Kubla Khan", the name has been synonymous with philistinism, with plodding indifference to art. With a characteristic taste for mischief, Potter made his Porlock a scientist. And not just any scientist, but one investigating an artist. Professor Porlock is an eminent cryogenicist lobbing "neuropeptides" into the brain of the writer Daniel Feeld to stimulate his memory and serve it up for inspection. She is a bolshy, sardonic dominatrix, a bitch to work with, whose bark is only slightly worse than her bite, apathetic to the terrorist agitation that surrounds her and, in the script at least, described as "withered and probably in her late sixties".
De la Tour took her on less out of enthusiasm for the part than from the realisation that this was her last chance to act in a Potter play. "I was always upset that I hadn't. I love Potter because he's very theatrical. He writes lines." And yet the actual filming was as far from the theatrical experience as she has ever trespassed. For the usual budgetary reasons, rehearsals were practically non-existent. And De la Tour loves her rehearsals. "I do like my little journey in my five weeks' rehearsal and it all grows slowly and develops." ("You can't hurry her," Mathias says. "She goes at very much her own pace.")
Nor was Potter's dialogue, a bewildering amalgam of neurological terminology and his own futuristic gobbledegook, like anything he'd ever written before. "I'm deeply impressed with all those actors in ER," she says. "When you play something full of language that you don't use - I mean it could be Japanese - and you're literally learning it almost phonetically, there's no way I could do it without having some sense of what I'm talking about. If anything needs rehearsal, that does." And then there were the chairs, amphibian contraptions that glide about the laboratory, apparently motored by sensory will, that were "technically hell, because other people were working them".
Still, it's a great part, and De la Tour in her blonde mop and flapping robes has made it even strangely glamorous. And though she made her name playing all these needy, manless women - from Miss Jones to St Joan - she's on to her third redoutable character in a row (following Les Parents Terribles and Three Tall Women); a case of three tough women. And the Poliakoff will be a fourth - also, oddly, a scientist. You can't see many emotional weaklings in Callas or Cleopatra or Ranyevskaya either. "People get very caught on a line," she says. "I think it's to do with where I am now - my age - showing a strength that I haven't shown before. 'Oh yes, get Frankie. She can be strong.' I chose to play very, very vulnerable people, then people defined that as a type, like spinster or wallflower, or even plain. It was never anything to do with that: it was just about extreme vulnerability, which I found fascinating. Obviously it's a part of you which you want to explore."
The other lure of Lazarus was the fact that it was filmed in Pinewood and shot like a movie. De la Tour has always been thoroughly theatrical: growing up in Bloomsbury, aged seven she would swan down Tottenham Court Road in a sari from the dressing-up box. Her mother, moving among poets, called everyone "darling" and so did her daughter. And her favourite exhibits in the British Museum were the mummies, the only ones in costume. But she was actually drawn to the profession by film. "I saw Marlon Brando in On the Waterfront and I thought, 'That's what I want to do'." Apart from Rising Damp, the movie, "the only films I've made were the worst films that were ever made in Britain." (Wombling Free, if you're interested, and Our Miss Fred with Danny La Rue.)
She might have read the runes in her father's career. Charles de la Tour was a documentary film-maker who forayed into B movies - there was one with Lloyd Bridges called The Limping Man - and made commercials for Pearl and Dean. "One day he said, 'I've just done a Camay and I've met a beautiful girl,"' and it was Julie Christie [who gets a big scene in the last part of Karaoke]. He wasn't hugely successful. He loved what he did but he had no ambition."
When De la Tour's parents divorced, her mother, who'd never worked, got a job buying lingerie for Marks and Spencer. Then she married a businessman, and the family moved to "this huge house on the river with marble basins" in Cookham. The plotline of marital breakdown and maternal penury was repeated in De la Tour's own adulthood. "It's funny how often that happens." In the same year, 1983, after huge success in Duet for One and on the fringe, her father died and the job offers dried up. She went into analysis and stayed there for 10 years. "It was extremely helpful."
There's no doubt that her examination of a "feeling of loss" has enriched her professionally. "She's a brilliant comedienne because she's a true tragedian as well," says Mathias. "Like all brilliant makers of comedy she understands absolute pain and truth." (Pausing for a spot of amateur Freudian analysis, it's plainly interesting that one of her heroes, as a teenager, was Bobby Charlton. "He was very vulnerable and strong," she says: "that combination again." But surely it's more significant that, like her father was and her brother Andy is, he was also extravagantly bald.)
Because she once played Hamlet, it has become commonplace to describe De la Tour as androgynous. "We must squash this myth," she says. She didn't become the only modern actress to play the Dane because she felt impelled to explore her male side but because "I just wanted to play the universal person, a young, vulnerable, fucked-up rebel without a cause". Thanks to her genetic inheritance, she actually stood more chance of getting the role as a woman than as a man. Francis de la Tour would almost certainly have been bald, and so even more handicapped by looks than Frances. Or Frankie.
'Cold Lazarus' begins 9pm 26 May, C4; repeated 10.20pm 27 May, BBC1