Ready, steady, Gomez A fine comedic actress, she scored a direct hit with her surreal performance as a sexually frustrated sociopath HR manager in the BAFTA-winning hospital comedy Green Wing. And now Glasgow girl Michelle Gomez is poised for bigger and

At first our photographer is reluctant, but Gomez isn't going to let up. She and Sadie are like two lovers that can't their eyes off each other. The rest of the world might as well not exist.

The first time I saw Gomez in the flesh and in all her random absurdity was at the Scottish BAFTAs in the autumn. The 34-year-old stepped on to the stage to present the best comedy award and launched into a delivery of a few lines of a song which seemed either to be a distorted Gaelic or chance gobbledygook. In fact she was singing the lines, "Where is your Pingu? Where is your Pingu?".

This, she says, can loosely be translated as "Where is your penguin?", a lyric she had made up moments before in the absence of anything useful to say. The evening, she felt, had become too soporific and needed a quick shot of the bizarre. Gomez recalls that she turned to her co-presenter Steve Mangan (Dr Guy Secretan of Green Wing) and said, "I've had an idea." "He just crossed his hand over mine and said, 'No'. I've worked with him for long enough now to know."

For many the Pingu ditty was a highlight in a blur of routine speeches, a moment of delicious madness. "There were two camps, " she says.

"One that said, 'What's wrong with you? What's your problem? Maybe you should go and lie down on a chaise longue and speak to somebody.'

And the other camp was, 'That was beautiful. Where did that come from. It was a really beautiful piece of folk singing'."

The song was the kind of ejaculation that might have emanated from her character in Green Wing. Sue White, bored, sociopathic, sexually frustrated staff liaison officer, who hardly exists outside her office, sits behind her desk as doctors come and go, inflicting her distracted lunacies on them all, then telling them to "f**k off". It doesn't sound like much, but in almost every scene there's a flourish of surreal, elusive comedy, a strange facial tick, bizarre noise or ludicrous puzzling aside.

Gomez is one of the star turns of a ground-breaking series littered with talent. Green Wing is unlike any other comedy or hospital drama, a show in which hospital staff are mostly demented and what matters is their frustrated dysfunctional sex lives, not their patients. To be the oddest of this cast of peculiarities requires quite some talent.

This, I suppose, is the bit in the interview where we would normally ease into discussing the career and life history of the actor, except we are not. We are talking about the dog. Sadie, once called Jet, arrived at Battersea dogs home in a patrol car, the orphaned companion of a convict who had been sentenced life. It had been calculated that by the time he got out she would be dead, so she was surrendered to the home.

Gomez and her husband, This Life actor Jack Davenport, had been looking for a dog, and were 'matched' with her, taken past all the other doors, two hopeful adoptive parents, straight to her kennel. "She was the only dog that looked at us with her back to us, " she recalls, "sort of saying, 'Move on, you're not going to want me. I've shat myself and there's much prettier dogs out there.'" Having long been a cat person she is now a convert to the dog. Cats, she says are nice enough, but a dog gives back so much more. "I said give us one that might die soon because we had never had a dog before. And now I regret that. I never want her to die.

Gomez has an unpredictability and an eruptive wit that lends itself to improvised comedy. Almost every answer she gives is twisted with a small gag. Asked whether she is in contact with Sadie's previous owner, she says, "I'd love to write to him in prison and say, 'Your dog's fine. She doesn't have mange any more'." It's as if we are riffing out a scene for a new show. Lately, she says, almost all her work has tended to be quite improvisational. Currently, filming Feel The Force, a comic "Cagney and Lacey meets the Sweeney", in which she plays a police officer who is "totally rubbish", she finds she can't resist what she calls topping and tailing a scene, adding in her own quirks and additions.

The method has been with her since the first series of Green Wing in which it was encouraged. "Basically we were given outlines of our characters and then we got into a room with a large writing team, eight of them, and we were basically given scenarios and allowed to play with them. Sue, I think, started out as a one-scene character and then turned into something else and we couldn't get rid of her."

Since childhood, Gomez has always been attracted to slapstick and physical exaggeration. Buster Keaton, Lee Evans, Lucille Ball. "I can't seem to deliver a line without falling down. You know it's very physical for me, it's not very subtle. You're never going to hear, 'Michelle Gomez? It's all in the eyes. It's all very contained.' It's not. I'm slapdash." Marti Caine, she says, was her biggest inspiration as a child. "Any woman that I could relate to that has a face as malleable as mine. I would think, "Ah, look, there's somebody else like me". I've always been a gurner. I tried to reel it in. You know there was a period when I thought I was going to be a really serious actress, but the gurning. . . I can't get in control of it. It just runs away with me."

It's often said owners and their pets look alike. Gomez doesn't have quite the sleek fur coat on the pining eyes, but there's something they share that combines sophistication with a touch of neediness. From a distance they both seem a little bit meaner than they actually are. At first I thought Sadie was a bruiserish chav dog ("a bit of a yardie dog, " says Gomez). I saw the Staffordshire and not the Lab. Similarly Gomez at first seemed just a little bit scary. She has a prickling manner.

I had been told she didn't want any personal questions. I assumed that meant questions about her marriage to Jack Davenport, which recent reports had suggested was on the rocks - though she still wears a wedding ring - but, personal also seems to mean questions about her twin brother which cause her to turn silent and sigh. Personal appears to be almost anything outside work. I've heard Gomez doesn't like interviews. That much is clear. Conveniently the make-up preparation seems to extend into the photo shoot, stripping down the time available for talk. "I don't like all this, " she says at one point. I can tell, I reply. No wonder Sadie becomes so much the centre of attention. It is easier, it seems, to interview a dog.

For all her spikes, though, it's hard not to warm to Gomez. There's a charm in that stinging humour and those strange leftfield comments. At one point I remark, like some gushing schoolgirl, on her great bone structure. "You fancy me, " she says. At another she explains to me that she has never liked to answer the question, 'what do you do?' with 'actress'. In the early days that was because she was still working as a waitress, doing her time on "two soups" and "would you like bread with that?". But, even now, she still likes to shrug it off. "I tell people, " she says, "I own an industrial Buffin manufacturing Company. I've said it for years. It's a conversation stopper."

The conversation pauses.

"What is a buffin?" I ask.

"A buffer."

"A buffer. . . like a buffer. . . what kind?"

"It's wholly uninteresting."

"But I don't even know what a buffer is."

"You know, for buffing floors."

Actress is still a word she finds hard to say. "I don't think of myself as an actress, " she says, "I still think I'm fannying around in my mum's front room." Even though she's now appeared in The Book Group and Carrie And Barry, has a part-share in the Green Wing BAFTA and has worked on a couple of films, she feels a little fraudulent. She laughs when the films are mentioned. "They all go straight to DVD. Whenever I try to take them out, the guy at Blockbusters always says, 'Oh, I wouldn't try that, have a proper film'. I'm always slightly worried if I do a film and we're filming it in Luxembourg. I know it's going to go straight DVD."

She only uses the word actress when trying to explain to me that she is not a celebrity and does not subscribe to that culture. I ask her what, in her view, a celebrity is. "Somebody who doesn't have any talent or skill or anything you might want to buy other than their personal life. And why would you want to buy their social lives? That's what you are doing when you buy these magazines."

But doesn't she buy them herself?

"Oh, I'm a total hypocrite. I'll sit and look through them. But the point is I always end up feeling like I do after I've watched porn. A bit mucky."

Gomez wanted to be an actress from when she was about seven years old growing up in Glasgow's southside and her parents took her to see Kiss Me Kate at the King's Theatre.

"I thought, wow, those people are showing off like me, that's what I do at home. I can do that and get paid. That was my first realisation that maybe I wasn't going to be a secretary or a postwoman or a lollipop woman. I did have a moment of thinking I liked the lollipop woman idea. But can you imagine? I would be like, 'F**king move your car!' I don't think that would work."

Her mother had been a model and ran a modelling agency called Browns Inc, and her father worked for a carpet manufacturer, which meant that they had "new carpets every year". They had met when he was a photographer and she was a model and he spotted her, elegant and fine boned, at a show. Born in Montserrat, the family left the island following the volcanic activity and, after being schooled by nuns on the beach in Antigua, he was sent to Fettes in Edinburgh. Gomez was one of four children, with two older brothers and a twin brother. I tell her I bumped into one of her brothers while tripping down the stairs at the BAFTAs.

"Derek, " she nods. "Tall and very good looking, thinks he looks like James Bond. He is, he's a head turner. I'll say it. He's a very attractive man."

I ask if those sharp cheekbones come from her mother.

"I'd like to think so, " she says, "but she's always saying to me, what happened?"

She is happiest when talking about her work. Green Wing was filmed in a working hospital, Northwick Park, just north west of London, a parallel world of cameras, cast and, alongside its everyday medical function. Gomez recalls that the staff seemed excited at first to have a film crew around, "but that only lasted about five minutes and then they got really pissed off because they couldn't get their gurneys down the corridor quick enough."

After a while they barely seemed to notice as she wandered round with a gladioli or rode the corridors on a camel. "It was like they became immune to us, we didn't really exist." Every now and again, because she wore a badge, a patient might ask directions, and she would send them off to the wrong department.

Outside in the snow, she smokes a cigarette. She seems distracted by the building opposite, a tattered wooden pub, which she comments looks like a barge. On its roof is a dog, poised looking over the edge. It seems she notices dogs in the way pregnant women notice babies.

"Yeah, I know, the baby thing, " she says. "I'm just happy with the dog."

We change subjects: quickly she seems to shuffle us on, past a door marked personal. Half the reason, it seems, Gomez doesn't like being interviewed is she doesn't feel she has enough to say.

"I'm an actress, " she reminds me, finally bringing herself to say it. It's as if she feels acting is not the most worthy of professions. "There are times when you come across somebody that's really impressive, someone that's got a proper living and really does make a difference to people's lives. Then I do feel a bit of a wanker, admitting I'm an actress. That's hard to say to someone who may be making a difference. But I don't know how I could change things."

From time to time she sticks her head back through the door to check on Sadie who whimpers and pines. It's as if she can't quite concentrate on anything else. When they say never to work with children or animals, perhaps it's because, like Sadie, they always steal the limelight. "It's a great distraction, " she says, "We really just want to talk about Sadie." But do we? Isn't it just Michelle Gomez, doting, obsessive dog mom, who only wants to talk about her?

I tell her it was a neat trick for a woman who doesn't like interviews to bring along a dog.

Green Wing series 2 starts on Channel 4 on March 31. Series 1 is released on DVD on April 3