There is a mechanical efficiency to the way she answers questions about Humans - the result, no doubt, of months of practice. Get her talking about her new favourite film, however - Pixar's Inside Out - and her brown eyes light up and an effusiveness emerges from beneath the veneer.
It's only when I mention her boyfriend, comedian Jack Whitehall, who she lives with in Notting Hill, that she bristles. "If I answer one question about him," she says, "it tends to become the headline and then my heart sinks."
Humans will have changed that. Indeed, you only have to stroll around London to see how much the series has increased her profile: her character's electric-emerald eyes (she wears contacts in the show) are everywhere, staring out from posters plastered across double-decker buses.
The show, which has been commissioned for a second series, has also been a success stateside.
"[Humans] has definitely had the biggest impact of anything that I've done," says Chan, who has previously had supporting roles in shows including Doctor Who, Sherlock, Fresh Meat and the hit indie film Submarine.
Filming Humans was far from easy, though. Chan had to somehow strip away all the nuances of human expression.
"At the beginning I thought my head was going to explode," she says, "because you're trying to play the scene and act truthfully in it but within the rules that you've set up for. As a human, you don't have to be too conscious of your movement. I think it's tougher playing a robot than a human, and even tougher playing a robot who begins showing traces of being a human."
As preparation for the part, Chan attended "synth school", where choreographer Dan O'Neill taught her the graceful and smooth movements needed to portray the cyborgs in the series
"The director didn't want anything robotic in a cliched or a jerky way," she says. "I was given a lot of homework: I had to practise ironing as a synth, practise washing up as a synth, cooking a meal as a synth. It's definitely the most prep I've had to do for a role."
Sometimes the obstacles Chan faced while playing Anita were more literal, such as a table or a set of stairs.
"At the wrap party," she says, "they showed the out-takes and it was like Humans the Sitcom, with a load of clumsy robots bumping into things. In an early scene, I was going down the stairs with a basket of washing and, of course, I wasn't allowed to look down. I miscounted the number of steps and suddenly just fell out of the shot. The crew pissed themselves laughing."
The themes of the show - mankind's hubris and looming obsolescence - follow the familiar contours of countless sci-fi stories. And yet, right now, they couldn't be more timely: Stephen Hawking and Elon Musk, among others, this year warned that the development of full artificial intelligence "could spell the end of the human race", while, in June, the first entirely robot-staffed hotel opened in Japan.
This is partly why Humans and Alex Garland's film Ex Machina have proved so popular with viewers, says Chan. "The technology doesn't feel like it's 100 years away anymore," she remarks. "It's practically here."
Who would be her ideal synth? "I'd want one like Samuel L. Jackson," she says. "If I ever got into any tricky situations, he could just stare people down. Parking ticket? Just set Samuel synth on them. That would be amazing."
