Eve’s trek into movies
ALICE Eve is fishing in her pocket for her iPhone to find me a picture.
She's just been to Russia on a promotional tour for what is easily the biggest film of her career to date - J.J. Abrams' sci-fi sequel Star Trek Into Darkness - and the blonde Brit wants to show me a gift she was given, a set of specially commissioned Russian dolls featuring the images of Kirk, Spock and other Star Trek characters.
"Isn't that genius?" she beams, proudly showing off memorabilia that would probably fetch a fortune at a Trekkie convention.
With this in mind, studio executives at Paramount will be relieved to know the 30-year-old actress didn't steal anything from the bridge of the Starship Enterprise - "I'm not a klepto!" she giggles.
Not even a uniform? "The fabric is very expensive," she trills. "They're almost artefacts."
Sporting a quite stunning mint-coloured mother-of-pearl frock coat - decorated with a swarm of bees - she simply seems delighted to be cast in one of this year's most anticipated blockbusters.
"It's a very special moment in my career trajectory."
Eve plays Dr Carol Marcus, a character who last appeared (as played by Bibi Besch) in 1982's Star Trek II: The Wrath of Khan.
Then she was a molecular biologist and mother to Captain Kirk's only son.
Here, joining the Starship Enterprise as a weapons specialist, there is a slight frisson with Chris Pine's Kirk.
But her mind is on higher things, with the crew fighting Benedict Cumberbatch's villain.
"She is a genuine superbrain," Eve said. "I just took it that she was as clever, if not the cleverest person on board."
There may be a slightly gratuitous shot of Eve in her bra - even Abrams can't resist the sexy scientist cliche - but the actress admirably convinces as a brain-box.
She did, after all, read English at Oxford. "(So) I'm not intimidated by academia. I pursued it quite heavily myself … and I went all the way with education."
Confidence is something Eve radiates. Until Star Trek Into Darkness at least, Hollywood may have tapped her up for a rather uninspiring selection of roles - the love interest in romcom She's Out of My League; Charlotte's "boobtastic" nanny in Sex and the City 2; Edgar Allan Poe's damsel in distress in The Raven and a young Emma Thompson with Sixties bouffant hair in Men in Black 3.
But there's far more to Eve than that. Not many would have the guts to walk into a room with Tom Stoppard and Trevor Nunn, and leave with a part in their production of the former's play Rock'n'Roll - "a good moment," she says.
The daughter of actors Trevor Eve (of Shoestring fame) and Sharon Maughan, Eve has almost circumvented the traditional "costume drama" route taken by most British actresses.
Her screen debut may have been a brief appearance in Richard Eyre's film Stage Beauty, but there's barely a petticoat or lace glove on her CV.
Rather, echoing her childhood - when her family moved to Los Angeles for her to try to crack the US market - she made a deliberate play and left for America.
So, what has it taken to break into Hollywood? "Dedication and being sure of your dream and following it with steadfastness, with an absolute focus," she says.
"I was clear about what I wanted to do and the world I wanted to be a part of."
While her accent is pure Home Counties, "I was an American girl," she admits.
"I had to come back here and learn to be English. I spoke with an American accent and I liked American things. And when my parents moved back, I had to learn what English girls spoke like and what English girls liked."
Having worked with J.J. Abrams, the acting bug's only going to get worse.
The director behind Lost and Super 8 has just committed to taking on the next Star Wars episode. And you can bet she'll relish brandishing a lightsaber if Abrams came asking.