In fairness, McGovern has known fame. In her twenties, she was a Hollywood ingenue, starring in films such as Ordinary People and Ragtime, for which she received a Best Supporting Actress Oscar nomination. At 23, she was engaged to Sean Penn, her co-star in Racing with the Moon.
"I've been through the fame thing so many times before that I've built up my system to contend with it. So now, in terms of Downton, I can't honestly say that it has changed my life much at all. I live very much as before, without any kind of fanfare. Perhaps if I'd gone into the show at 20, it would be different."
In person McGovern, 53, is polite, and porcelain-skinned. Experience has cautioned her against easy explanations for Downton's phenomenal success. In the country of her birth, for instance, it is regularly watched by 17 million viewers.
"You'd imagine that, being American, I'd have some clue why it's so big in the States, but I haven't. Maybe they like it for the same reasons we do - because modern life is so frenetic, we all crave a world that's slow and solid."
Cleverly, too, she says, Julian Fellowes writes period drama for the contemporary brain. "So the scenes are short and move quickly from one story to the other. The drama rocks along, which modern audiences like."
In the new series Cora's storyline includes a flirtation with a new character, Simon Bricker, an art historian played by Richard E Grant. A friend of the Crawley family, he starts sniffing around the ancestral pile admiring more than the priceless oil paintings.
"Oh, it was so much fun to work with Richard again," McGovern says. "But then he's been a friend since we worked together on The Scarlet Pimpernel in 1999."
The on-screen flirtation, she says, will tax Cora's marriage to Robert (played by Hugh Bonneville). "But the real conflict comes from their very different attitudes to change. Robert's entire world is based on tradition, so he feels incredibly threatened by the arrival of Ramsay MacDonald's Labour Government. But Cora, of course, is an American whose money only arrived in her father's lifetime. So change doesn't frighten her at all. But it's the differences between them that bind them and that's the case in a lot of marriages, isn't it?"
She has formed a strong bond with all of her screen daughters - including Laura Carmichael, who plays Lady Edith, and, before her departure, Jessica Brown Findlay, who played Lady Sybil. "Filming the scenes in which Sybil died in childbirth was incredibly tough," McGovern says. "Normally, you can't wait to get your teeth into big emotional scenes, but I dreaded them because, as a mother myself, I didn't want to put myself in the devastating space of losing a daughter."
Off-camera, the relationships with her screen daughters feel less maternal, and more a friendship of equals. "We are compatriots, and I've learnt as much from them as they've ever learnt from me."
TV profile
Who: Elizabeth McGovern
What: Downton Abbey season 5
When and where: Prime tonight, 8.30pm
See: TimeOut TV picks today for five things to know about the new season
