"There's a wicked bar in Hackney I was working in so I'd probably still be there," she tells me with a laugh, adding: "Game of Thrones was the creation of my career. It opened all the doors."
It has led to the starring role in Breakfast at Tiffany's on the Broadway stage and now to Hollywood and a major role with Arnold Schwarzenegger in Terminator: Genisys, the fifth installment of the science fiction action drama which was launched in 1984, before the 28-year-old British beauty was born.
She has also recently finished two other movies and we talk about her life and career in a suite at the Four Seasons Hotel in Beverly Hills.
Emilia is on crutches because, she says: "I fractured my hip, like an idiot." But she avoids revealing how the injury happened, saying frivolously: "Arnold was trying to show me a dance move and I took it to a whole new special effects level, so that's the result." Then she adds: "I'll be off them soon. It'll be all right."
In Terminator: Genysis Emilia has the iconic role of sharpshooting murder target Sarah Connor, who is protected by Schwarzenegger's T-800 terminator, known as the Guardian. Sarah Connor was played a generation ago by Linda Hamilton and Clarke knows Terminator fans will be scrutinising her and comparing her to Hamilton.
"It was a double-edged sword for me because one of the reasons I wanted to take the role is that I grew up being inspired by Linda's brilliant Sarah Connor , so as an actress I jumped at the chance," she says. "But it was only later that the pressure of what I'd taken on dawned on me. In Game of Thrones I'm lucky enough to play a very strong woman who doesn't really get her hands dirty, so I came to this movie with none of the skill sets I needed to play Sarah Connor.
"I had to learn a lot, namely the gun training; I had military advisers helping me out and I really wanted to beat the boys so I made sure I was training enough to have the strength to be able to last a day's filming carrying those guns and trying to impress the guys."