It was 60 years ago that Rita Tushingham made her film debut in A Taste of Honey. “I’m expecting a gold clock or something,” says the 79-year-old actor over the phone from her London home. In the absence of a commemorative timepiece, the anniversary will have to be marked instead by a new movie set partly in the decade in which she became a star. In Last Night in Soho, Edgar Wright’s fantasy-horror, Tushingham is one of three 1960s icons (Terence Stamp and the late Diana Rigg are the others) who lend the film prestige and authenticity.

I wonder how it feels to personify an entire era, but she isn’t telling. “Can you imagine walking around thinking, ‘Ooh, I’m an icon’?” she scoffs. “It would be dangerous. It’s just nice that people know your work from that far back. Terence still looks fantastic, doesn’t he? The extraordinary way he walks! He’s like an old bear claiming his territory.”

Tushingham stars as Peggy, the grandmother of Eloise (Thomasin McKenzie), a fashion student who pitches up in modern-day London from Cornwall and is spirited back to mid-1960s Soho in her dreams. During her own early years, Tushingham played an array of similarly wistful outsiders drawn to the capital – in the comedies The Knack … and How to Get It and Smashing Time, or the clammy 1972 thriller Straight on Till Morning.

She made the journey to London herself in 1961, upping sticks from her home city of Liverpool, where she was earning a pound a week as an assistant stage manager, to act for Tony Richardson at the Royal Court. This was after she had already auditioned successfully for his film of Shelagh Delaney’s play A Taste of Honey, in which she was Jo, the headstrong, working-class Salford lass living with her gay chum while scandalously pregnant with a mixed-race baby; Richardson had turned down an offer of Hollywood funding that was contingent on casting Audrey Hepburn in the lead instead.

Audiences were seduced by Tushingham’s naturalism and dazzled by her searchlight eyes. Even in her 70s, they still pop cartoonishly, though she has never seen what all the fuss is about. “Some of my brothers’ friends used to call me Cross Eyes. You know what boys are like, they’ll do anything to get attention. People told me I had these large eyes but you don’t notice it yourself.” The most she will concede is that they are “useful to have when you’re in closeup”.

At the start of Last Night in Soho, Peggy warns her granddaughter that London can be “a lot”, though that seems not to have been Tushingham’s experience. “Everything exploded and London was at the centre of it. But at the time I thought, ‘Ooh, is this what London’s always like? It’s quite nice.’” Her friend and Taste of Honey co-star Paul Danquah, who played the father of Jo’s baby, introduced her to Francis Bacon. “We went out to supper after the premiere. They took me up these dirty stairs to Muriel’s club, full of these flamboyant people who, being from Liverpool, I hadn’t mixed with before. And I went to Francis’s studio. I’m so glad he was part of my life.”

What was different about being an actor in the 60s? “There wasn’t that sort of panic you have today over whether something is a great success in case people give it rotten tomatoes. You could go home and be away from all that. You could have a private life.”

Several films she made in that period featured some sort of progressive content. The Knack …, with its use of rape as a comic subject, has aged poorly, whereas The Leather Boys, in which Tushingham plays a young bride whose husband grows overly fond of one of his biker mates, still has a daring tinge. “It was quite brave, wasn’t it?” she says. The picture’s Canadian director, Sidney J Furie, suffered an anxiety attack on set. “It was during the Cuban missile crisis. Sidney said, ‘OK, that’s it. We’re all gonna die. We’re not shooting any more today.’ It wasn’t exactly high spirits! So we all went home.”

Kitchen-sink dramas began disappearing down the plughole. The following year she was in Madrid shooting Doctor Zhivago with David Lean, and going for long walks with her co-star Alec Guinness, who would push funny little notes and doodles under the door of her hotel room.

She met Princess Margaret at the London premiere. “We were all told to wear gloves,” she gasps. “Then at the New York one, we walked this red carpet with balalaikas playing all the way along. Someone asked me for my autograph, and when I looked up, it was Stirling Moss. Isn’t that incredible?” Her habit of soliciting agreement at the end of each anecdote would be touching enough, though she also sounds freshly wonderstruck, as if she has just that moment stepped off the red carpet, the balalaikas still jangling in her ears.

This is all well and good, but one of the messages of Last Night in Soho is that nostalgia never tells the whole story. Sleepwalking into the 60s, Eloise witnesses the woes of a young singer, Sandie (Anya Taylor-Joy), who is trying to break into showbusiness but encountering only creeps and crooks. It’s a portrait that rings true for Tushingham.

“We all knew people who were being exploited,” she says. “It hasn’t stopped, has it? But we’re far more aware of it now, thank God. Back then, it was done sort of quietly. People accepted the fact that young girls were abused. They’d say, ‘Oh he’s just like that, don’t worry about it, he’s a DOM.’ That meant Dirty Old Man. Isn’t that awful? It sounds like an honour or something.” How did she survive? “I was tough. I’d been brought up with two brothers so I could fight and I didn’t take any nonsense. In Liverpool, we stand up for ourselves.”

She wouldn’t tolerate bad behaviour even when it came from major stars. Take the 1966 action movie The Trap, in which she has to chop off Oliver Reed’s gangrenous leg with an axe. “I was quite happy to do that,” she says wryly. Was Reed a handful? “He tried to be, but I just didn’t take any of his shit. I handled him. And he knew that from day one, so there was respect between us. When he wasn’t trying to play games, he gave some brilliant performances. I got on very well with him.”

What about his view, which he proudly declared to Johnny Carson in 1975, that women’s liberation would never last? “Oh, Oliver would say anything to get a rise. Peter O’Toole, Richard Harris – they were all of a certain school. They sort of tried to outdo each other. It was acceptable in those days. Funny, isn’t it?”

By the beginning of the 70s, some of the stars of the previous decade were scratching around for work. Stamp reflected in 2015 that “when the 1960s ended, I just ended with it”. Did a similar fate befall her? “What happened was that they weren’t making a lot of films,” she says. “There had been so many. ‘A spy film was successful, let’s make four …’ The money wasn’t there like it had been.”

She acted in a handful of pictures in Italy in the 70s, and enjoyed the bustling way of working over there. As long as they paid her, that is. “I was doing a film in Italy and the money hadn’t gone into the bank. They called me: ‘Rita, come to set!’ I said, ‘You put the money in, I’ll be there.’ It was the opening scene, so I was in a very strong position. I didn’t do it to be ballsy. If I see something is wrong, I’ll say so.”

There have been quiet patches, but there is usually some bright-spark director (Carine Adler with Under the Skin, Nick Moran with the underrated Telstar) who needs those eyes, that febrile presence, that swinging 60s baggage. Tushingham can currently be seen as a troubled landlady with some unpleasant views in Ridley Road, the four-part BBC series about fascism in 60s London, though it doesn’t feel to her like six decades since she was really there, rather than pretending to be. Neither would it be accurate to say that time has whizzed by in a flash. “More like a couple of thunderclaps,” she says. Funny, isn’t it?

• Last Night in Soho is in cinemas from 29 October. Ridley Road is on BBC iPlayer