Playing William Shakespeare is no mean feat. And it's a role that it certain to make Joe Fiennes a household name.

He is already seated at a corner table at a trendy pub a few streets away from his newly purchased flat, when I arrive for our chat. Joe Fiennes is particularly difficult to spot and then I realise why: the baseball cap crammed on to his head is half obscuring his most famous assets - those absurdly dreamy hazel eyes that are making women all over Britain swoon.

The cap stays firmly put (as does his leather jacket) throughout our two-hour conversation, but his bashful allure - at times, he resembles a faun caught rather sweetly in the headlights - doesn't wane for a minute. You're tempted to think that it might be an act, but it soon becomes clear that this is part of 28 year old Joe's appeal - he's simply not practised enough at the publicity game to give journalists a rehearsed performance. Indeed, if Joe had his way, he wouldn't bother much with journalists at all.

But any recluse routine Joe plans to conduct in the future will, for the moment, have to wait. Since his supporting turn as Robert Dudley, Earl of Leicester, in last year's film, Elizabeth, the boy is, as they say, hot. In his new film, Shakespeare in Love, he co-stars in a romantic comedy smash that is tipped to topple Saving Private Ryan at this year's Oscars. Already John Madden's film is up for six Golden Globes, among them a Best Actress aware for Joe's co-star, Gwyneth Paltrow, who recently broke up with one of the film's other stars, Ben Affleck. But cinema's hottest heartthrob is still coming to terms with all the attention, much of which has focused lately on his love life. After ending a six year relatioship last year with actress Sara Griffiths, he has now been linked with Braveheart star Catherine McCormack.

As well as Shakespeare, Joe has two new film projects on the go plus the American release of Martha - Meet Frank, Daniel & Laurence, the popular three-boys-in-love-with-the-same-girl film in which he starred with Rufus Sewell and Tom Hollander, still to come. Are we to expect a bit of a Joseph Fiennes festival, then? 'That's the scary thing,' says Joe, tucking into his haddock fishcakes. 'That's why I get a bit worried and concerned, because I've put in a lot of work, particularly in the theatre, and I just get concerned when people think 'Oh, he's just got the job because of x, y and z'.' X, Y and Z being his brother Ralph, presumably? 'Mmm,' comes the mumbled reply.

Not that anyone would be likely to confuse the two. While Ralph gives off a slightly glacial intelligence, Joe emanates a kind of laid-back warmth, characterised by a ready laugh and a rather endearing spaciness. His manner is kindler and gentler, more puppyish than his famously intense brother. There's also an eight year age difference between the two, and, says Joe, although Ralph has helped him get a foot on the ladder, the two lead entirely separate lives.

While Ralph went to RADA, Joe chose London's Guildhall, which he left in 1993 before graduation to pursue his professional career, a year behind Ewan McGregor. Joe recalls that when Ralph first took note of his aspiration 'he gave me the complete works of William [Shakespeare], with a lovely inscribed note; it was very, very supportive.' And in producer David Putnam's 1992 television film, A Dangerous Man, Lawrence After Arabia, in which Ralph played the title role, he saw to it that Joe got a cameo part.

'People say 'When are you going to work together?' but the point is that we already have. I had three seconds where I'm just in the background. That was really kind of Ralph; he got me on to do that.'

Among his five other siblings, Joe is closest to Jake, his twin, a gamekeeper and 'the only one,' says Joe, 'who has a sane life.' Another brother, Mick, an archaeologist, was fostered by Joe's parents and is now accepted as a fully fledged member of the Fiennes brood. 'Our mum,' says Joe, 'always said she knew from the age of 12 she wanted six kids, so she had six and fostered one.'

The remaining three are all involved in the arts in various ways: Martha has made her directorial debut with the forthcoming film, Onegin, produced by and starring Ralph and with a score by brother Magnus, a musician who has written songs for All Saints. Sophie, a sister, is a producer and writer who has worked over the years for dancer and choreographer Michael Clark and director Peter Greenaway.

The creative gene evidently existed in the Fiennes family even before the current crop - their father was a photographer and their mother a writer who died of breast cancer before the publication of her recent book Blood Ties. 'We were all geared, I suppose, towards the same territory,' says Joe. 'Since the age of dot it's never been a surprise what the thrust has been.' Born in Salsibury, Joe moved with the family 'about 15 [now it's 15 ?!?] times' before leaving school to attend a one-year art course in Suffolk. His peripatetic childhood fed his acting instincts. 'It must have started then, really - the ability to communicate, to reinvent yourself in order to survive at school. That's a great warm-up for acting.'

The solitude of his mother's literary life also played its part. 'Mum felt that writing was perhaps the most isolating form of work. She impressed upon me how lucky you are to be a part of a team, an interactive process that is just a joy; she thought one should relish that.'

Although Joe appears to have just burst upon the scene, his career has progressed in much the same steady, measured way as brother Ralph's. Both served long stints at the Royal Shakespeare Company, and Joe recently returned to his stage roots, earning £200 a week playing a laddish North Londoner in Nick Grosso's Real Classy Affair. 'Theatre allows you really to stretch yourself. There's that joy of being able to do parts on stage that you could never do on film simply because the camera doesn't lie,' says Joe. 'Somehow the myth and mystery and magic of the theatre as a medium can take you in all different directions.'

And yet even on stage, Joe got cast as the dogged young swain, an image that carried straight through to Martha - Meet... and to his pining Will in Shakespeare in Love. Small wonder, then, that Joe talks fairly dismissively of Martha - Meet...: 'It's good fun, sweet and harmless, [though] whether I'm here to do sweet and harmless, I don't know.' Shakespeare in Love is sweet, too, though anything but anodyne with a screenwriting credit from none other than Tom Stoppard. Joe was first approached for the film while he was still at drama school, after Daniel Day Lewis had pulled out and the then director Ed Zwick (Glory) was looking for someone to appear opposite Julia Roberts. 'My puritanical drama school streak was going 'God, you can't do a film about Shakespeare and make it comical',' says Joe. Nonetheless, he was put up for the role but Roberts pulled out, preferring a different leading man. 'I was terribly tight-assed about Shakespeare and having the proper respect. Then it all sort of came back five years later, and I thought 'This is strange, yeah,I'll read it.' The structure remained the same, but the dialogue had changed. It's a great exploration of how love can inspire. So we don't really dwell on Shake-speare himself; it's about where he got his inspiration from. The film goes from the charming to the hopefully quite moving.'

After Elizabethan England, Joe's next move brings him right up to date as a psychotic mob accountant in the eagerly awaited Rancid Aluminium, based on James Hawes's cult novel. After that, he joins Gretchen Mol (Rounders) in the film Forever Mine, playing an American in Seventies Miami who gets shot in the face.

Despite the prospects of these high-profile roles, which will inevitably be accompanied by more recognition, Joe seems desperately keen to hang on to his relative anonymity, which, he insists, was essential to his role in Shakespeare in Love.

'I'm fortunate in that I'm not known, which is quite nice if you're taking on a great historical figure. If it's played by someone we all know is a celebrity, it can be very difficult to believe they are inhabiting a part.'

But Daniel Day-Lewis has that ability and, interestingly enough, he almost played the Shakespeare role himself. 'He's not a celebrity,' counters Joe. 'The point is, he really acts.' And as he takes his leave with a farewell wink, Joe leaves no doubt which of the two - celebrity or actor - he would rather be.