"Young people tend to think that they have the prerogative of this online dating thing,” says Francesca Annis, “but a lot of people my age do use it – they just don’t talk about it very much.” The actress, who has been a star ever since she played Elizabeth Taylor’s handmaiden in Cleopatra (1963) as a teenager, is now 74. “I know people who’ve gone on to marry and have long-term relationships. It’s very positive.”

Would she use it herself? “I haven’t but I think it sounds very interesting,” she says. We’re chatting over tea in the low-lit surroundings of a basement café in a London hotel; Annis, immaculately dressed and made-up, is radiating certainty in a soft, polite voice. She’s just about to appear on our screens in ITV’s Flesh and Blood, an unusual hybrid of crime and family drama, emotionally engaging and with a great cast, in which she plays the mother of three adult children – mirroring her own life (“Vivien’s got two grown-up daughters and a son, I mean, no acting required!”).

Unlike Annis, though, Vivien is recently widowed, and in the first flush of new love with Stephen Rea’s rather oleaginous surgeon, whom she met online. As in the BBC’s recent Gold Digger, her children immediately display varying degrees of suspicion of his motives, especially financial ones. I wonder if she thinks it’s common now for children to have anxieties around their parents’ romantic choices?

“Do you ever get rid of anxiety about anything, let alone one’s family?” she returns. “People can be very social and welcoming, but when [someone] is actually going to step right inside, I think people in general become quite anxious.”

There’s an unhappier comparison with Annis’s own life in Vivien’s revelation that her ex-husband “was no angel” and had pursued an affair. Annis has never married, but she had a 23-year relationship with the photographer Patrick Wiseman (the father of her children) and then an almost-10-year relationship with Ralph Fiennes, 17 years her junior, which ended in 2006 amid rumours of his infidelity. Does she think that it’s possible to forgive affairs or do they leave an indelible mark? “I’m sure that they leave a mark… anything that’s been a huge upset to you in your life is part then of your make-up,” she says.

She’s just returned from a long trip down the Amazon, where she stayed in the rainforest with a tribe of indigenous Ashaninka people – with a friend who has worked with them for 20 years. Annis’s mother was half-Brazilian and she lived in Rio de Janeiro as a child, where her parents ran a nightclub on Copacabana Beach. Both were actors, her mother, who was from a wealthy family, also a singer.

It’s fascinating being with her. Here in the room, Annis carefully self-edits around any subjects that might be considered contentious, but I sense just beneath the surface is the freewheeling child of the Sixties: iconoclastic, opinionated, free.

Annis was right at the heart of the Sixties scene. She lived with Texan folk singer Shawn Phillips, who introduced her to stars of the era including Jimi Hendrix and Mama Cass – “we would jam through the night and things”. Donovan lived on the top floor of their house and wrote a song about those days – Sunny South Kensington (“Jean-Paul Belmondo and-a Mary Quant got / Stoned to say the least”).

Did Annis do the whole Sixties drug-taking thing? “I’m not going there,” she says, quickly. And we’re back with the Francesca of today. “I’ll take that as a yes,” I laugh.

She’s defined by the idealism of the era, though. “Feminism has had a lasting impact on everyone’s lives,” she says. “I don’t think anyone can say that the women’s liberation movement was just a cult that came and went. It’s had a huge effect on young women’s lives, and life in general, men’s too.”

I want to know how she regards the Harvey Weinstein trial. She’s cautiously considered again – “I think the law is there to protect people against exploitation and people who have been exploited should have justice” – less so on her own experiences in the industry. “I’m not saying that no one ever made a pass at me. That would be not true, but nobody ever overstepped the mark with me and I was not backward in putting out the vibe: ‘Don’t even think about going there.’”

She actually had the opposite problem with the singer Prince when she appeared in his directorial debut Under the Cherry Moon.

“He was deeply religious in spite of being this very sexual performer,” she says. “We were meant to be having an affair. But he didn’t want to kiss me on the mouth because I’d had children; that was against his religious beliefs. So I suggested the most old-fashioned thing: ‘Look, Prince, we can swan round behind the sofa, and then as you approach me, we can just sink down behind it’ – which he thought was a brilliant idea. It must have been used a million times. From then on, he just thought I was great.”

Was he sexy? “I thought he was,” she says. “I mean, how can you not find someone sexy who’s so brilliant?”

Annis’s career really took off in the Seventies, a decade in which she would succeed on stage and screen, playing a famous Juliet opposite Ian McKellen in 1976, as well as an Olivier-nominated Cressida in the same year, and twice gaining nominations for a Bafta before finally winning in 1979 for her portrayal of Lillie Langtry in Lillie. She began the decade playing Lady Macbeth in Roman Polanski’s blood-drenched adaptation of Shakespeare, a role which she tried to turn down, but was convinced to take on.

Filming started little more than a year after the murder of Polanski’s pregnant wife, Sharon Tate. Annis hasn’t seen Quentin Tarantino’s Once Upon a Time in Hollywood, which revisits the events leading up to the crime, but she remembers Polanski at the time clearly. “He would talk about his Sharon… things like, ‘Oh, Sharon and I did this or that.’ It wasn’t as if it was taboo to ever mention the name, but he never talked about the murder.” He made no reference to Lady Macbeth’s speech about the knife, she adds, but when filming the murder of Duncan’s sons, he overruled the set designers, ‘I know what it’s like, I know how much blood there is.’ And he just threw it everywhere.”

Didn’t she once refer to Polanski (who fled the US in 1978 while awaiting sentencing for unlawful sexual intercourse with a minor, and has been accused of sexual assault by several women over the years) as a misogynist? “No, no, no, no,” she says. “… he didn’t take much notice of women when you were around… [but in his] portrayal of women on screen, he’s always interested in their psychology. That’s why I did Macbeth… He’s a great film-maker. It’s a great loss that we haven’t been able to have more films from him.”

She laments the way that cinema is being usurped by streaming. “I’m personally heartbroken that so many people watch films at home. I think you don’t get the full experience.” She went to see Little Women recently, and admired it immensely, but says there was hardly anyone in the auditorium. Should its director, Greta Gerwig, have been on the all-male Bafta shortlist? “I haven’t seen all the other nominations. It’s quite hard to be judgmental.”

Flesh and Blood, I might add, is written by a woman, Sarah Williams, and directed by another, Louise Hooper.

It clearly emphasises that Vivien and Mark’s relationship is a sexual one. Does Annis, who has played romantic leads throughout her career, think that people downplay their sexiness as they get older? “No, I don’t think they do actually,” she says. “They’re not out there flag-waving, that’s the point.”

Flesh and Blood starts on ITV on Feb 24 at 9pm