You could say that Rigg is still favoured by fortune: now 67, she stands with Judi Dench and Maggie Smith in that triumvirate of dames who can draw a West End audience. She stars there tonight as the betrayed wife in Honour, by Joanna Murray-Smith. It's a play that creates a vivid, disturbing portrait of a marriage breaking up. Has she found it upsetting to work on?
Rigg takes that question to refer to her divorce from Archibald Stirling in 1991. "D'you know, incredibly not. My marriage broke up 15 years ago; 15 years is a very long time.
"Um..." she continues sonorously, hesitating for the only time in our interview, "obviously there are moments of recognition. Various bells ringing along the way. During rehearsal, I suddenly remembered the emptiness of the house. The sense that a presence had gone."
Rigg patrols her privacy carefully - she was once described by the director John Dexter as "about as vulnerable as the north face of the Eiger" - so this gut response is a surprise, but she is not about to divulge all. "I will never write my autobiography," she tells me. "Never; never ever. It would have to be about myself, and I couldn't bear to write about myself like that. Other people would get dragged in too - and that would be very bad manners."
Rigg was born in Doncaster and brought up in Jodhpur, where her father, dubbed Sahib Rigg, worked as an engineer. She was sent back home to boarding school at seven, and then progressed to Rada at 17. As a classically trained actor, she did the expected thing and served at the RSC, before doing the absolutely unexpected thing and donning a catsuit on television for the role of Emma Peel in the psychedelic spy series The Avengers, appearing in 51 episodes between 1965 and 1967. It made her an instant star and an icon of the Sixties. She surprised everybody again when she made the transition back to Molière, Albee and Euripides - via the least successful Bond film of all time, On Her Majesty's Secret Service. She became a dame in 1994.
Rigg wears her achievements lightly. Today, she slurps carrot-and-coriander soup (she is on her lunch break from rehearsals for Honour), speaks fondly of her co-star Martin Jarvis - "He's got a wonderful teddy-bear-ish quality. Very easy to cuddle, you know?" - and draws with relish on her Marlboro Light. One gets an inkling of the sense of fun that led the young actress, appearing semi-naked on stage in Tom Stoppard's Jumpers in 1972, to entertain the actor playing the dead McFee by writing messages to him on her body.
But now she is an actress of age and stature - a grande dame - don't people expect her to be terribly dignified? No, she says. "Gone are the days when older people were granted respect because of their age. People no longer stand on ceremony or dignity. Nor should they."
She continues: "If I was just looking out for myself in a production, I'd be reviving a tradition in theatre which is long dead, where the... old actor comes on and does their thing and treats everyone else like... midgets. It used to be like that in my day. I didn't dare talk to Dame Edith [Evans]. I don't think she'd have encouraged it."
Dame Diana, by contrast, tries to be approachable. "And encouraging. It's very much one's duty to be encouraging to young talent." Even going so far as to attend fringe theatres? "Certainly," she says. "I go to pub theatres like the Fin-bo-rough." (She delivers the word like an extended arpeggio, rather in the manner of Edith Evans. Perhaps it is a pity she recently turned down the role of Wilde's Lady Bracknell in the West End.)
"But you have to be careful, because young people nowadays don't really like advice, as I've learnt to my cost." Rigg pulls a face of mock-pique. It's clear she is referring to her actress daughter, Rachael Stirling. "She doesn't come to me for advice. Ever. I'm not allowed to give her notes. I've had to learn to..." she makes a gagging motion, "zip!"
Watching Stirling on stage, one cannot help but be reminded of the young Rigg. Doesn't Rigg find the similarities, vocal and physical, uncanny? "Well, yes," she concurs, sotto voce. "To be honest, I do! Though she's absolutely her own person, and her approach to what she's doing is very different from mine."
But back to the dignity question. There's a moment in Honour when Claudia (the young love rival of Rigg's character, Honor, played by Natasha McElhone) tells her: "Dignity's your thing, isn't it? The older woman's singular advantage." Does Rigg take that as a put-down or a commendation? "I really don't care what people think of me," she says crisply. "My manners are good. I do care about people's feelings, but I'm so far beyond caring about anything else. There's a wonderful freedom in being my age."
Rigg is slightly irritated and acknowledges, "I can be scary. I know I can. It's something I've always had. When I lose my temper I can be very scary." Thinking of the play in hand, she likens her character to Sylvia Plath, although she also feels she must not be too fierce. "I think I might have to watch it a bit."
For Rigg's terrifying and thrilling performance as the child-killing Medea, at the Almeida theatre in 1991, there was no holding back. "She was so terrifying because her character was defying predestination. She was defying the gods. She was utterly outside civilisation, with her kind of primeval savagery." Where does Rigg's ability to communicate such primeval savagery come from? Did her mother have that power? "No," she says. "No one in my family had it. They were all adorable. I don't know where it comes from. Maybe it goes back to growing up in India.
"We had a terribly ghetto-ised childhood, never allowed out to the bazaar unaccompanied, you know - but I think you still pick things up. Children do. I remember in Jodhpur, I must have been about five or six, my brother and I used to go down to the bottom of the garden, to try and look over the wall at the world outside. Well, one day there was this terrible silence all over the town, like there had been an earthquake or something. I found out that one of the last women to commit suttee had done so that day. I picked it up from the gardener, or the ayah. The goddess Kali, creation and destruction in a great big fireball - what a wonderful idea.
"You know how people find the poverty in India appalling, the beggars appalling, the misery appalling? Well, I don't. I don't find any of it appalling. It's absolutely explicable in terms of that continent. Not to say that one wouldn't want to do something about it - raise money for charity or whatever - but acceptance of it is a part of the Indian outlook. I understand that."
Rigg enjoys life outside work. "When I'm not working, I'm perfectly happy," she says. "I'm travelling; I'm in my house in France, which I am still working on." She has a Jack Russell, Mabel. She learns French. She doesn't watch much TV (reality TV, she thinks, demeans its participants and is watched, in the main, by people who despise humanity.) She goes to the theatre ("I'm shameless. If I have to drop a name to get seats, I will"). She plays bridge, drinks Campari, smokes. And she doesn't take on a role if she doesn't want to.
'Honour', Wyndham's Theatre, London WC2 (0870 060 6633) to 6 MayReuse content