Mamie Gummer on The Collection and her mother, Meryl Streep

“Mum, without blinking, gave me her leather jacket, put it on over the costume and wiped my make-up off,” says Gummer now, nearly 20 years later. “It was that transition [from childhood to adulthood] that’s so difficult for kids, made within the space of 20 minutes. And she was there on both sides of it. She’s a great mother.”

Mamie Gummer, Rick Springfield and Meryl Streep

She is also, it should be said, Meryl Streep. Gummer, 33, is the second of Streep’s four children with the sculptor Don Gummer. It’s hard enough having one of the most famous women in the world as your parent, but now that Gummer is an actress in her own right, with her latest role in the hotly anticipated Amazon Prime drama The Collection, it becomes even more awkward. Did she ever want to do anything other than act?

“If I had, I would have done it,” Gummer says drily.

As it was, she grew up in Salisbury, Connecticut, a first-hand witness to her mother’s success. The year she was born, Streep won her first best actress Oscar for Sophie’s Choice. When she was two, her mother was starring in Out of Africa. By the time Gummer was 12, Streep was in The Bridges of Madison County. And that’s before you even get to Streep’s roles in The Hours, The Devil Wears Prada, The Iron Lady or Mamma Mia!.

Gummer, by contrast, has had a quieter ascent. She started out in school plays and was in two produc
tions of Arthur Miller’s The Crucible (“I was an intense kid”). After graduating in 2005, she enjoyed critical acclaim in a number of Broadway plays before moving to the small screen.

She played Nancy Crozier, the mischievous lawyer in The Good Wife, and took on the part of Sally Adams in the 2008 HBO series John Adams. There was a short-lived stint as the lead in the American medical drama Emily Owens MD, and she has appeared in a few films, too – Lasse Hallstrom’s The Hoax in 2006 and last year’s Ricki and the Flash, which also starred her mother.

Her younger sister, Grace, is also an actress and has appeared in The Newsroom. Youngest sibling, Louisa, is a model and older brother, Henry, is a musician who has also been in a few films. It seems to run in the blood. But when we meet in a private members’ club in London, it’s clear she wants to be taken seriously in her own right. Questions about her mother are politely deflected. She is guarded and reserved, even a touch cold (although this might be shyness).

She’s at her most relaxed when talking about her work. In The Collection, an eight-part drama set in Paris after the Second World War as the city emerges from Nazi occupation, Gummer plays Helen Sabine, a divorcee who has remarried the head of a fashion house. In the taster video clip I was allowed to see, the clothes look fabulous.

The Collection is pegged to be the most fashionable drama since Mad Men

“Yes! It gave me a kind of architecture,” she says. “The undergarments particularly: it was different and you sort of altered your posture.” She wore a wig for the part, “which helps with the process. I spent more time in hair and make-up when I played Emily Owens, where it took one-and-a-half hours to perfect her normal hairdo.”

Gummer has always been “fascinated by uber-feminine characters, because it’s quite alien to me.” In person, she has a striking look – an asymmetrical face, pale, freckled colouring and a faraway expression in her flinty, blue eyes.

She finds it difficult to watch herself on screen: “The first time you see yourself, it’s ‘Ugh! The left side of your face is weird’, or ‘Why is one tooth longer than the other?’”

Is there a lot of pressure for women to look a certain way in her industry? She nods.

“It’s confusing because you’re meant to be vulnerable [as an actress] and then you have to have the skin of a rhinoceros when walking down a red carpet, being scrutinised. There’s definitely a conflict of interest but it’s worth it – the trauma of self-promotion is completely undone when you get the job and do the work.”

Today, she’s wearing low-heeled suede boots and jeans and appears fresh from a massage without a scrap of make-up. Her features are delicate. Her hair is almost white-blonde. The most colourful thing about her is a dazzling silver and floral-patterned coat that she keeps on throughout the interview.

“We spend a lot of time covering up how we’re feeling,” Gummer says. “Clothes can be part of that. With acting, we get to release that. Everyone in this show is covered up so it’s about excavating what’s underneath.”

Although The Collection looks glamorous, it was mostly filmed in Swansea, and Gummer spent a lot of time shuttling to and from London on a train. “I found it pretty reliable and very comfortable,” she says. Besides, she likes Britain, especially the light and “even the weather. I think it comes from my background. My people are very, very white and not wild about the sun.”

In fact, she has Norwegian, German, Swiss, Dutch and Irish blood. She lived in Los Angeles for a bit for career reasons, but found it “creatively stifling. There’s an infectious desperation in the air. I was going to lots of SoulCycle classes and juice bars, and not working.”

Gummer gets asked “all the time” whether she’s European. Partly it’s because her American accent is faint. She reminds me of Katharine Hepburn, in the way that she speaks and her reserve: she has that sense of being far older than her years. “It’s just occurred to me I’m not a girl but – I’m going to sound like that Britney Spears song now – I’m still a young woman. I feel pissed off when people say ‘ma’am’ but I was never comfortable with the ‘ingenue’ thing. I feel like I’ve lived a bit.”

She got married at 27 to the actor Benjamin Walker and divorced two years later. Now in her 30s, Gummer feels “more settled”.

“All my world wisdom,” she says. “I can’t help it – I just collected it for better or for worse”

Having been brought up by a strong woman, it’s no surprise to learn that Gummer is supporting Hillary Clinton for the 2016 Presidential bid. “We can’t allow Trump to lead our country,” she says.

Clinton, by contrast, “has the experience necessary. She has compromised in certain ways and surprised people in the ways she hasn’t.” There’s a pause. “Also, I really want to see a woman lead the United States.”

It’s not such a stretch of the imagination. She’s been raised to believe women can do anything.

The Collection is on Amazon Prime from today