The film, adapted by Tom Stoppard from the Second World War - set novel by Robert Harris, sees Scott, who plays star code-breaker Tom Jericho, team up with Winslet's frumpy Hester after her housemate and his obsession, Claire (Saffron Burrows) goes missing. The co-producer is Mick Jagger.

For Scott, however, an intensely private fellow, it must be a troubling time. When we meet at the Edinburgh Film Festival, where Enigma received its European premiere, he has his publicist sitting in the interview with him - a warning sign to any hack with a list of personal questions. He is at a critical career juncture. After a stint on Soldier, Soldier launched him, the success of British films such as Twin Town, This Year's Love and Regeneration helped him slide into Hollywood fare such as Ever After and Deep Impact, before snagging the plum role of Tom Cruise's villainous adversary in last year's blockbuster.

Undoubtedly hard-working, Scott has done little else since coming off the long-gestating production for MI:II - which, due to reshoots and a shoulder injury he sustained, meant he lost out on the juicy role of Wolverine that Hugh Jackman later claimed for X-Men. An artistic director at the Donmar Warehouse, he recently played there for American Beauty director Sam Mendes, in the First World War drama To the Green Fields Beyond, having already completed Enigma. He has since wrapped Ripley's Game, which sees him play the victim of John Malkovich's eponymous trickster, in yet another cinematic outing for Patricia Highsmith's literary creation. Due to start work on an adaptation of Dylan Thomas's Map of Love, again for Mick Jagger, he is also co-producing a movie about those notorious republicans Oliver Cromwell and Thomas Fairfax, which will see him star as the latter.

I do what I feel is right at the time, he says, robot-like. Opportunities come along, and I take them or I don't. I feel happy about what I'm doing, and I work instinctively. Hopefully I'll be able to continue that. Scott behaves much as Robert De Niro is reputed to. He lives the character, and has no desire to reveal his own personality in public and spoil the illusion.

Now 35, this blue-eyed boy rivals Ewan McGregor as the British film industry's most bankable male export. But, bar the fact that he is a passionate Hibernian FC fan and changed his name from Stephen to Dougray for Equity reasons, the Fife-born actor is well known for guarding personal details. Why would anyone want to know about my childhood? he asked one reporter. What's important is whether I'm any good. I'm interested in talking about the work. All the other stuff I find bizarre. I find it intrusive.

For Enigma, a complex but rewarding drama, Scott spent five months mentally limbering up to play his character - a man he says goes from being lost- but-innocent to being tormented by the codes and the woman that haunts him. Aside from visiting Bletchley Park, the operational nerve-centre where the film is set, and reading Harris's novel more than 10 times, he watched documentaries on the Second World War, read books on code-breaking, spoke to Oxbridge mathematics professors and Bletchley couples, and even set about dismantling the Enigma code-machine. I took it apart hundreds of times, so that I could put it back together, he admits. I enquire whether, to play the insomniacal Jericho, he adopted Dustin Hoffman's trick of staying up for three nights to affect exhaustion in Marathon Man. I didn't sleep very much during the film anyway. That's what I do, get obsessed about it. I just get into the rhythm of the character; it's easier for me. I don't like acting things; I like feeling things. Mentally, you get attuned to whatever the situation the character is in, and that affects the physicality of the character.

A method man ever since he trained at the Welsh College of Music and Drama, Scott is a serious actor, not one lured by the glamorous lifestyle Hollywood has on offer. While his marriage may have gone the way of many Tinseltown unions, it's more likely that extreme commitment to the job caused a break-down in relations than affairs of the heart. Like Jericho, Scott is a man devoted to his craft; women, on the other hand, remain an enigma.

Enigma (15) opens on Friday