I am witnessing Man in Kitchen. Dominic West is attempting to make coffee. "What, no coffee?" he rails at the heavens with a bellow that puts Brian Blessed to shame. "Aha. Coffee," he roars triumphantly, producing a foil-wrapped package from the fridge. "Oh no. It's cheese," he deflates. We decide on tea and he declares Assam to be the thing and starts fiddling around with loose leaves while delving into drawers for a strainer, finally settling for a large sieve which causes spillage and necessitates much mopping up. We wander out into his garden to sit on some banged-up red benches.

Last time I met Dominic West, four years ago, he was among those tipped for the Bond job that went to Daniel Craig. "I was pretending to be laid-back about it," he says, 'but I absolutely would have loved to have done it. Also, though, there was a school of thought - that I was trying to subscribe to - that it was a bit of a poisoned chalice because the films had got so bad. You forget now because it's so good. I think a few people would have paused before accepting it. I would have paused for about half a millisecond before reluctantly taking up the mantle. It was all looking a bit dinosaur-like before Daniel Craig came along. He's a good actor and it makes all the difference."

But as Daniel Craig was beginning to win acclaim for his brutal secret agent, Dominic West was on his own, more discreet trajectory, grafting away for six months each year on the set of a little known Baltimore police drama, The Wire, which was initially aired on the subscription-only HBO channel in America. Playing hard-drinking, lecherous avenging angel Irish cop Jimmy McNulty, he started filming in 2002 and completed the fifth series in 2007, even though, when he expressed doubts about living in Baltimore for five years, he was reassured the show would never be commissioned beyond the first season. "They couldn't get anyone else to do it," he says now. "I was trying to get out of it at every stage. No one was watching it and I'm superficial in that way. I wish I could say I knew this was great, important work but I didn't care. I wanted lots of people to watch it and I wanted to win awards. I did win one once. For 200m swimming."

The popularity of The Wire, so named because of the telephone tap the police use to catch criminals, grew, cult-like, through DVD box sets and illegal downloads until, this year, Londoners began to catch on, although here TG4 screened it from 2003 to 2008. The entire 60 episodes have recently begun to be broadcast on BBC Two, but Barack Obama has declared it his favourite show, and numerous publications, including Time magazine, have named it the best television drama of all time. "There is a sense among people who have watched it that they are part of a secret society," says West.

Created by crime journalist David Simon, the programme looks at the underclass in Baltimore, the corrupt policing, the rampant drug trade, the soaring murder rate, the shady politicians, the shabby journalism and the inadequate resources. "David is extraordinary," says Dominic. "He is this short, fat Jewish guy with a big head and you can just see the brain. He's brilliantly articulate and incredibly kind and democratic and I think he is, without doubt, one of the greatest writers alive today."

It is not an easy watch, though. The language is hard to follow, emotional pay-offs come at the end of each series rather than each episode and the dramatised reportage style is both confusing and wearying, but it is immensely satisfying and has lifted Dominic's image beyond that of vaguely interchangeable, almost famous, public-school hottie and given him status, credibility and marketability even greater than Clooney's in ER. And look what happened to him. Dominic has that rare quality of looking lithe and luminously handsome or heavy-featured, simian and menacing depending on the day, the lighting, the character. I do not think he is a vain man.

He has long been known around Baltimore where the population, police and dealers watch The Wire ? the latter, they say, to get tip-offs on how the police are tracking them; it's that realistic and well-informed. His fame spread across America and now he is regularly stopped on London streets. "My favourite was on this beautiful sunny evening when I was walking down the street in Queens Park [where he lived until recently] and there were these three incredibly cool-looking people walking down the middle of the road laughing gaily and there was this beautiful woman, backlit and so glamorous, and she looked at me and went, 'I love you!' I nearly collapsed. And it was Zadie Smith." Another time, coming out of a Tube station, he was 'badged' by a policeman who told him that a lot of the Metropolitan police force watch the show and only wish they had similar resources. "That is something, seeing as the whole point of the show is that they have no resources."

He denies that his time playing McNulty has given him any kind of sixth sense or X-ray vision when it comes to seeing street deals and dodgy interactions that you or I might miss. "The difference between a good policeman and a bad one is an ability to read the streets," he says. "I went around with them quite a lot and they can tell, from tiny signs, what everyone is doing. Poncing around pretending to be a cop doesn't quite cut it." He does, however, point out supposed crack houses on his street and says that the fast food joint at the end of the road is a "crack supermarket".

Nonetheless, this corner of Shepherd's Bush has an old-fashioned blustery, blossomy Victorian charm on this spring morning. He moved to this house last October with his girlfriend, the Irish garden designer Catherine Fitzgerald, their two-year-old daughter Dora, eight-month-old son Senan and, part of the time, his nine-year-old daughter Martha, from a relationship with Polly Astor that ended when Martha was two. He and Catherine, a glowy rose of a woman who used to be married to the Earl of Durham and whose father is Desmond, 29th Knight of Glin, are expecting another child at the beginning of June and their airy house over-flows with baby paraphernalia.

They first got together at Trinity College Dublin but she left him shortly after. They remained part of the same group of friends and reconnected four years ago. "We've been trying to get married for the past three years but then another baby comes along and ruins it," he says. "So we've decided to do it very simply. Catherine's parents own Glin Castle in Limerick, and she kept saying, 'We'll just do a register office and the pub'. I said, 'We could do that... or we could go to your castle.' Anyway, she's won and we are going to Hammersmith register office and then the pub round the corner."

The children are coming so fast, perhaps he hopes to match his own experience of growing up as one of seven. "It's impossible," he says. "I don't know how my parents did it. I remember when Martha was born and I took her on a plane for the first time, it was so exhausting that I wanted to die. My parents used to take us all to Majorca on Dan-Air and my dad would pack enough milk and cereal to last a month."

Dominic was brought up just outside Sheffield, where his father had a successful business making bus shelters and bath panels and the like. He was the second youngest and the only child to be sent to Eton. The other boys attended Ampleforth like the good Irish Catholics they were. He started acting at Eton and Damian Lewis, who was a couple of years below him, said recently that Dominic's performance of Hamlet in a school play was the best stage performance he has ever seen.

West studied English at Trinity College Dublin before embarking on a three-year postgraduate drama course at the Guildhall. As soon as he left, work started to trickle in, his father had a liver transplant and his parents split up after 30 years of marriage. His father moved to Ireland. "He went there because he thought my mum would follow him," says Dominic. "She's always said that she wanted to live there so he thought that if he went and got some idyllic place then maybe she'd come." She didn't; neither did she remarry. She still lives in the Yorkshire house that Dominic grew up in.

"Dad had ten good years after the transplant and then he died within three weeks. It was odd because they told him the operation would give him ten years and he was a very religious man and he was always trying to work out what he was here for. As far as I was concerned, I had an amazing time with him then. He always had ten years in his sights, and it was almost to the day that he checked out."

He lived long enough to see Dominic build a career firmly rooted in the classical theatrical tradition. On film, he played Lysander in a star-studded A Midsummer Night's Dream (with Christian Bale, Michelle Pfieffer, Kevin Klein and Rupert Everett) in 1999, and gave a sweaty, low-life turn as Renée Zellweger's sleazy boyfriend in Chicago in 2002. He graduated to the romantic lead opposite Julia Roberts in Mona Lisa Smile (2003) and there have been a few movies slotted in since, but it has mostly been about The Wire, which is set to serve him well.

He has just finished filming Centurion, in which he plays the Roman general Virulus, commander of the legendary ninth legion who were called in when no one else could do the job. In this instance, they were summoned to crush the Picts, and all 3,000 of them charged into Scotland and promptly vanished.

"Actually there is recent archaeological evidence to suggest that they were somewhere else all the time, but don't tell anyone that," he says. He likes a costume and a horse and gave an impressively unhandsome performance as Oliver Cromwell last year in Channel 4's The Devil's Whore.

He talks longingly of giving his Dane and doing a musical. "I think my singing is marvellous but no one else seems to." Judging by the booming in the kitchen, I imagine it to be an intimidating baritone. "I really wanted to do Guys and Dolls. They're doing it in New York and they really wanted me. Then I started singing and they didn't want me at all," he laments good-naturedly.

He has turned down more American television work because, at the moment, he can't bear to be away from Catherine and all those children for extended periods of time. "Cecil Day Lewis said that the enemy of good art was the pram in the hall," he says. "But look what was in that pram ? Daniel Day Lewis."

Indeed, nine-year-old Martha West made her film debut last year, playing the daughter of Charles Darwin (Paul Bettany) in Creation. "It's not something I'd instantly want my children to do," he says, "but she's always said she wanted to do some acting, and my agent suggested it and Polly said yes, so I took her along to the audition so she could see how hard it is and what a nightmare it is and she blew the doors off." Much like her father, perhaps Martha is destined for seemingly effortless success.

Having finished Centurion two days ago, he is still happily bearded and says he is delighted to have nothing in the diary beyond the birth of the new baby. But he is in an interesting position and the next few jobs will be crucial in terms of building on The Wire's remarkable cultural presence. He talks of theatre and musicals and all that nice, pure, actorly stuff, but surely it will be Hollywood where the tangible sense of superstardom that surrounds him will be cemented and actualised. He has recently been in Los Angeles for meetings and I suspect that, with The Wire as proof of pedigree, he will soon command top billing. James Bond? Who needs him? Certainly not Dominic West.

The Wire is currently showing every night on BBC Two at 11.20pm