The Bletchley Circle star Rachael Stirling: I never asked my mother Diana Rigg for acting advice

Stirling is 41, but so disarmingly direct that she seems much younger, studenty even, as she’s wearing a black cotton dress and what might well be a charity-shop overcoat on what is a ferociously hot day. She is also slightly hungover. “I was hanging out with my beloved Jules yesterday and I had too much wine. But I’ve washed my hair and brushed it. And I don’t brush.”

Her “beloved Jules” is Julie Graham, co-star alongside Stirling and Anna Maxwell Martin in the ITV series The Bletchley Circle, which ran for two series in 2012 and 2014 and was a fictionalised account of former wartime codebreakers solving crimes in the early 1950s. It’s now being resurrected (without Martin) as The Bletchley Circle: San Francisco. The new series relocates Stirling and Graham to California, where they form a new crime-solving team with two ex-wartime US female codebreakers.

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The new series starts, as crime drama apparently must, with the horrible death of a woman. “But then the plot takes a turn,” says Stirling. “Jules and I told each other that we wouldn’t do it again if it’s about women being locked up in basements, half naked. We really meant it. And it’s not. We’ve shaken it up and made it jazzier and more interesting, more racially diverse.”

Stirling was supposed to have made it big 16 years ago, when she starred alongside Keeley Hawes in the BBC’s Victorian lesbian drama Tipping the Velvet. “I remember somebody saying, ‘Ooh, I bet Keeley goes on to do loads of things and the other one doesn’t,’” she says. “And that’s pretty much what happened. I have a theatrical career, which has stood me in good stead, but I haven’t been on that sort of huge television takeover that Keeley has accomplished. But that’s the thing, you’ve got to keep on truckin’.”

She says “the arrogance of youth” stopped her from asking Rigg for advice after Tipping the Velvet. “I haven’t talked to my mum about it since. She’d only say the thing that we’d both say, which is – it’s not a sprint. Mum’s on Broadway, about to turn 80, and she’s just been nominated for a Tony. It’s a marathon.”

For Bletchley, Stirling has mastered middle-aged, midcentury posh, and in real life she has a voice from a Powell and Pressburger film and the bearing that comes, like it or not, from six years at Wycombe Abbey, the prestigious private boarding school for girls.

Actually, she didn’t like it at all. “I was very homesick for the first year,” she says. “I was slightly the weaker one of the pack and, girls being girls, they smelled blood. I think I became a bit ‘OCD’ in order to cope with being away from home – I’d pull my socks up to under the knee.

“In my last two years, I was rebellious. I was suspended for impersonating somebody’s mother on the telephone to our housemistress – I got up to appalling things. I had a boyfriend nearby and I would just run out of the school grounds at ten o’clock at night, go to his house and come back in time for chapel at 8am.”

She didn’t go in for posh boyfriends, despite the efforts of her father, the Scottish millionaire Archie Stirling. “My dear dad always tried to introduce me to children of his friends, but I just never took to them. Those were the people we were shoved with at school dances, usually Eton boys because it was the cleverest boys’ school, and ours was supposed to be the cleverest girls’ school. We were known as the ugly school, so it was, ‘It’s your lucky day!’ when they were ushered in. We used to dress in bin bags as a sign of rebellion.”

Did she like any of the Eton boys? “Well, Rory Stewart [Conservative MP and the Minister for Justice] used to do the Gay Gordons.”

Stirling says people still see her poshness before they see the person within. “The way I sound and where I come from means that sometimes I’m judged before I get there. If somebody takes against me, I try not to cry into my soup. You want people to like you, or at least not to judge you, and that’s not always the case. But that’s somebody else’s folly, and I just try to navigate my way through it. I don’t sweat it.”

Did she tone down for Garvey’s family in Manchester? “No, not at all! I was so nervous when I met them. I was trying to impress Guy’s mother, Shirley. But it was like meeting family, I just loved them.”

Garvey and Jack went with her to Canada for The Bletchley Circle: San Francisco, Garvey working on new songs as she filmed. “He was writing the whole time we were there. Some of it’s absolutely amazing, prompted by his walk to the studio every day through an area of Vancouver called Gastown, which was like Night of the Living Dead – in the middle of the day. It’s terrible, you see people jacking up on the corner of the street, lesions on their faces, barely managing to stand up. I’ve never been into drugs, I’m partial to the odd joint, but I cleaned up my act after we went on honeymoon and I found out I was up the duff.”

The couple had a nanny on set for Jack – did her mother do that? “She kept work very separate,” Stirling says. “So, I wasn’t hanging around famous people. My mum says I never had tantrums. I had elongated and very complicated tea parties in my cot, and I was sort of talking, I guess, quite young, and I would say, ‘Oh, how lovely to see you, do come in!’ I’d have these theatrical tea parties by myself with my imaginary friends.”

And now she’s still playing with imaginary friends. The great appeal of Bletchley, she says, is the camaraderie of the female leads. “We used to say to ourselves, ‘We’re superheroes! Superheroes with brains. Superheroes with handbags.’ And I thought, ‘That’s a pretty good thing to be putting out there. ‘Superheroes with handbags.’”

Rigg is bound to be far too busy to read this. But just in case, I’d say she didn’t mess up.

The Bletchley Circle: San Francisco airs on Wednesdays at 9pm on ITV