As I sit down with Millicent Martin in her lunch break from rehearsal, a handsome, bronzed man approaches our table. It is Topol. He and Martin make an inspired pairing: two household names from the 1960s, about to co-star in Gigi at the Open Air Theatre in Regent's Park, playing the roles immortalised by Maurice Chevalier and Hermione Gingold. Had they ever worked together before, I asked, prompting an “Ah yes, I remember it well” moment for both. They had - in Martin's 1960s TV show, Mainly Millicent, they'd sung together: “Da da da da da in the morning, pom pom the bells are gonna chime,” Topol murmurs. “That song from My Fair Lady.”

“And Dudley Moore was on too,” Martin says.

“And that guy who told stories about Ensa,” Topol says. “Bruce Forsyth?” Alan Jay Lerner might have scripted it.

Topol is 72 and Martin is 74, a great joint advertisement for staying power. Neither minds if people associate them with what they sang 40 years ago: Topol has been singing If I Were A Rich Man in Fiddler on the Roof all over the world ever since, and Martin is for ever grateful to the late Ned Sherrin for “giving me my career” in That Was The Week That Was in 1962. “It was lovely to be a household name, and to be recognised. People ask, ‘don't you hate it?', and I say I'd start worrying if they didn't.”

Ned Sherrin first gave her pastiche songs based on news items when he produced the Tonight programme in the 1950s. “Ned needed quick studies, and he knew I was a quick study. On TW3 we would get the script Saturday morning and we went out live Saturday night.”

Except for the unforgettable edition after the night of Friday, November 22, 1963. During the morning rehearsal it became clear that this was no moment for satire. “Ned said go home and come back at 4 o'clock. By then, that amazing team [Sherrin, David Frost, Christopher Booker, Bernard Levin and Caryl Brahms] had put together a Kennedy valedictory programme.” Martin sang In the Summer of His Years, a tear visible on her cheek.

There were only 26 episodes of TW3 and Martin is grateful that they don't get revived today. “When I said ‘Your flies are open' [in a sketch with Roy Kinnear] 18,000 people phoned the BBC in shock saying the country's going to hell in a handbasket. What would you have to say today to shock people? The show would just seem so tame in 2008. I'd rather it was just a memory.”

She was born in Romford, Essex, but her family moved to Tottenham when she went to the Italia Conti theatre school at 12. Most women in her family worked at the Klinger Stocking Factory, so they got their nylons cheap. Martin instead became “what the Americans call a triple threat - actor, singer, dancer - and the British call a show-off”.

Millicent Martin was the name she was born with. The same cannot be said for her once-long nose, which sat uneasily on her small face until she played Dulcie the boop-a-doop girl in The Boy Friend on Broadway in 1956. She came home after four years in New York with “a dear little purchased nose”. When she was 43 and her nose was 21 she planned to give it a birthday party - then she tripped and broke it. It emerged even smaller.

As Mamita Alvarez, Gigi's courtesan grandmother, she gets to wear gorgeous belle époque costumes with a Spanish flavour: polka dots, tailored jackets, leg o' mutton sleeves. “We all wear whalebone corsets,” she says, “that improve the posture no end.” Lerner stipulated that Ah Yes! I Remember It Well should be sung with wry amusement, not sadness or sentiment - “like Send in the Clowns,” Martin says. “And I get to do a little dance with The Night They Invented Champagne.” Martin's third husband, the American voice coach Marc Alexander, fell in love with her when she sang Sondheim's I'm Still Here in Side by Side by Sondheim the night it opened on Broadway in 1977. “I think it was the way I flicked my feather boa and lay across the piano.” They lived in Connecticut for 26 years, and moved to Hollywood when she played a ditsy rich lady in a soap. Now they have homes in Palm Springs and in Century City, the glamorous development on 20th Century Fox's former back lot.

“As you get older the good parts get less [four years ago she played the Bette Davis role in Whatever Happened to Baby Jane?]. But,” she says happily, “I've got to the stage where if something comes up I like, I work. If it doesn't, I don't care.”

Gigi, Open Air Theatre, Regents Park, London NW1 (0844 8264242, www. openairtheatre.org), from Aug 6-Sept 13

Editor's choice

• U2 at Nou Camp Stadium, Barcelona
• The 50 Best Movie Villains
• The 15 golden rules of theatre etiquette