McCartney, a 43-year-old portrait photographer, laughs as she recounts the plot. Her approach to taking pictures is just about as far removed as possible from Fannie's. "I'm always trying to make a connection with the person I'm photographing," she explains. "I don't want to just come away with a shot that I think is interesting – I also want the subject to like that shot of themselves. I won't go: 'That's great, it doesn't matter what you think, it's going in.' I want it to have a real sense of them."
It is an empathetic, sensitive approach to photography, but it is one that produces some stunning results. Subjects – particularly celebrities – appear to relax when McCartney turns her lens on them. The images often feel intimate and genuinely spontaneous, as if we are peering in on a private, unguarded moment. McCartney has selected about 50 of her favourites for a mid-career retrospective, entitled Developing, that opens this week at the Lowry in Salford Quays, Manchester.
McCartney was inspired to become a photographer in her mid-20s, sifting through contact sheets taken by her mother Linda. Linda Eastman, as she was, spent the 1960s documenting the rock'n'roll scene, mostly in New York, and in 1968 her photograph of Eric Clapton became the first front cover of Rolling Stone shot by a woman. Around this time she met Paul McCartney in London while she was working on a portfolio of the "swinging 60s". They married in March 1969, Mary was born not long afterwards, and Linda stopped taking professional commissions.
"My mum was quite a wanderer," says Mary. "She had a real sense of adventure and a cheekiness to her, which is something I like and that I try to take into my style of work. I remember once we went for an Indian lunch and I grilled her about her early career in photography and particularly about the people she was hanging out with. I was like: 'I can't believe you photographed Jimi Hendrix!' I was so jealous."
When it comes to working with exceptional individuals, Mary does not fare too badly herself. In Developing there are portraits of the artist Tracey Emin styled as Frida Kahlo and actor Gwyneth Paltrow dressed as a Blond Ambition-era Madonna, in cone bra and secretary headset; the Gossip singer Beth Ditto wears a Bardot wig and covers her modesty with a white sheet, while the Dowager Duchess of Devonshire, the last surviving Mitford sister, shelters from the rain at Chatsworth in Derbyshire.
"She's got a really funny side to her," recalls McCartney of her meeting with the Duchess in 2008. "You go to the loo and you find out that she's got all this Elvis memorabilia she collects. Then in the living room, on her side table, there's a little signed photograph from JFK: 'To Debo, love John.'"
Is there anyone she is still desperate to photograph? "Dolly Parton!" McCartney says, almost squealing. "I love her; I love her voice, her music. I imagine she's quite done – she'd probably arrive camera-ready – but I just find her life so intriguing."
It has not been deliberate, but the majority of the portraits at the Lowry are females – formidable ones. A decision was taken to devote one of the main rooms of the gallery to "radical women", including Helen Mirren, Vivienne Westwood, Vanessa Redgrave and Chrissie Hynde. "I've always been drawn to strong women," says McCartney. "When I like what they do, it makes me quite proud to be photographing them, and I feel an extra responsibility to show how cool I think they are or something. With Chrissie, she's one of my favourite people: she almost can't help herself, she is who she is – it's not made up. Beth Ditto's the same, it's not a made-up persona, she's just passionate about what she does."
McCartney has photographed many of her subjects on multiple occasions, but she finds it can often get harder rather than easier after the first time. "When you know someone, you have to get into a different headspace – it's easy to get distracted if it's too friendly," she says. One exception, though, is her father. "Dad's really good fun to take pictures of, because he likes to make it interesting for himself, he doesn't just want to do a straight portrait. So he'll mess around or say, 'Let's do something crazy with my hair.' If I'm doing it, he knows it's a safe environment and he can go further than he would otherwise, so you may get that one unexpected shot."
If Mary McCartney's professional life is dominated by women, then at her home in north London – where she lives with her four sons, who are aged between 13 and one, and her second husband, the filmmaker Simon Aboud – it is strictly men only. "There's not a lot of pink in my home, definitely," she says. "But I like the chaos, luckily."
Last year McCartney wrote a vegetarian cookbook titled Food, but she is adamant that her priority remains photography. She is currently working on a stills and video project called Devotion that focuses on people who dedicate their bodies and lives to their vocations. Ultimately the series may include boxers, priests and a Japanese geisha, but two sets she has already completed are the dancers of the corps de ballet at the Royal Opera House and performers from Le Crazy Horse erotic cabaret in Paris.
It's hard to think of two more contrasting groups, I suggest. "Actually there's not very much difference between the pictures," says McCartney. "The ballet dancers are very confident with their bodies, so they are not at all prim – it's actually quite gritty. And a lot of the women at Crazy Horse, their background is ballet. It's the same gruelling schedule and time commitments. You couldn't necessarily tell them apart."
Developing: Photographs by Mary McCartney runs from 16 March to 9 June at the Lowry in Salford, Manchester (thelowry.com)