"I always have this sense," says Tamsin Greig, "of 'whatever you say, you're going to sound like a twat'." Not the best start to an interview, perhaps, but in the few minutes we've spent together, in the café of the Jerwood Space where she's currently rehearsing, she has sounded perfectly coherent and perfectly polite. So where does that come from? Greig laughs, and her long, expressive face (which she says makes her look like a sad horse or a puffin, but which I think makes her look like Virginia Woolf) lights up. "From experience!" she says. "Scientifically speaking, if I say something, or it gets misquoted, or people put a spin on it... I mean, are you interested, really, in what people are saying?"

Hang on, love, I'm asking the questions here, and anyway everyone loves Tamsin Greig. They loved her in Black Books, they loved her in Green Wing, they loved her in Love Soup and they loved her when, after 10 years, she went back to the stage for the RSC. She seems, in fact, to have got "loveable" pretty much sewn up. "Yeah, unfortunately," she says. Unfortunately? "I don't know whether that's what I do to it. 'You're not going to be able to stop loving me', and that's the problem. Maybe I struggle with playing people that are unlikeable." But isn't that down to the characters she has played? She gives a grim little smile. "I don't," she says, "think the character in Black Books was very likeable. I somehow managed to make her particularly charming."

She did indeed make Fran Katzenjammer, the neurotic gift-shop manager neighbour of Dylan Moran's grumpy bookshop owner in Black Books charming, and Dr Caroline Todd, the neurotic doctor in the blissfully kooky hosp-com Green Wing, and Alice Chenery, the (yes) neurotic singleton shop assistant in David Renwick's specially-written-for-her BBC comedy drama, Love Soup. This happily married mother of three appears to have cornered the market in charmingly ditsy singletons, but her latest character, an LA theatre agent in Douglas Carter Beane's The Little Dog Laughed, isn't loveable at all. "She's so clever, and so manipulative and such a brilliant liar," she says, with what looks like wide-eyed admiration, "and I felt really nervous around her."

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But that, it turns out, is precisely why she took the part. "There are parts of this character where I think 'I just can't do this', because I can't imagine why someone would behave like this, but we all have an imagination, we have that beautiful part of ourselves, and it's mostly a very flabby muscle." Diane, the character she plays, is trying to suppress the truth about her client, a still-in-the-closet young movie star who falls in love with a rent boy. The play, she says, is about "the complicity of deception" and it's already clear, from the passion in her voice, and the vehemence of her desire not to be misunderstood, that Tamsin Greig is not keen on deception. What she's keen on is understanding, and truth. She's keen, it soon becomes clear, on understanding why a paedophile becomes a paedophile, or a serial killer a serial killer, or a hard-as-nails theatre agent becomes what might, on first appearance, appear to be a prime bitch.

She's keen, in other words, on doing her job well, but there's more to it than that. The act of "imaginative empathy" takes, she says, "time and energy". "To go to an art gallery, you can't do it in 20 minutes, you have to spend time going, 'where am I? Where are they? Where do we want to go?' Which is what one should be doing in art. Tapping into a moral compass." It is, I can't help thinking, quite brave, post Brown, to brandish a moral compass, but now she's talking about responsibility, and the audience's ability to respond, and how she got intrigued by that, and how she'd grown up "in a busy home where you don't always get a response".

Her father, apparently, was in his sixties when she was born. "He was," she says, "an Edwardian, and had no idea how to talk to three little girls." He did, however, love slapstick, a passion that Greig shared and developed while also acting in school plays. After a degree in drama at Birmingham, and a typing course undertaken at her mother's suggestion so she could "always temp" (which, for a while, she did), she worked in fringe theatre, got the role of Debbie in The Archers, supporting parts in a number of TV dramas and then, in 2000, Black Books. In 2004, she was in Shaun of the Dead, and the first series of Green Wing, and in 2005 she played a nurse in Doctor Who. That year, she juggled two small children and a baby with Love Soup, Green Wing, The Archers and Doctor Who. This is clearly a woman, to coin Cherie's phrase, who knows about having "a lot of balls in the air".

And then, in 2006, she went off to Stratford (with, amazingly, her husband's blessing) and gave an Olivier-winning performance as Beatrice, and a touching one as Constance in King John and then, in 2008, a blistering one in Yasmina Reza's God of Carnage and in David Hare's Gethsemane. The loveable, ditsy, TV stalwart had, in other words, shown that she was a proper, grown-up stage actor with an extremely impressive range. "I'm more surprised than anyone," she says, "to find myself where I am. Every time I look up, it seems to be an extraordinary landscape. I'm delighted, and a bit frightened."

Delighted, fine, that's nice, that's sweetly modest, but why is she frightened? "Well," she says. "I don't think it's a bad thing. Fear-mongering, where we're at at the moment in our world, is crippling, but to be frightened because you are not sure about your own capacity to engage with the event you find yourself in, is great. Take everybody out of their comfort zone!" And then she tells me about a book called The Pigeon, in which a man with an obsessive-compulsive disorder finds a pigeon in his corridor, which destroys his world, and how we're all given pigeons, which symbolise much more, and how her sister tells her when she's driving and wants to turn one way that she should always turn the other, because she's always wrong, and that sometimes it's really important "to have that little question there, should you be doing it, or the opposite?" It's all very charming, but it's also, I can't help thinking, just a little bit like a sermon.

And when I ask her if she thinks she's congenitally suited to acting, a famously insecure profession in which she has suffered very little insecurity, she agrees that she "can't really talk about the phone not ringing" and says that she has "been incredibly blessed" and that that "might be to do with the fact that we often get given what we can take". Do we. So does she, I ask, fighting the urge to scream that "what we can take" seems, in that case, to vary rather dramatically, mean this in a Christian sense? Greig, who was brought up an atheist, but converted to Christianity at 30, pauses. "You could," she says, "say that that's because I believe there's a personal God, but I think it's got more layers than that. What we have to do is receive the things that happen with grace, and I'm so glad I've got someone to thank."

We could, I tell her, be locked in theological combat all night, but we haven't got time, so instead I ask if her teenage acting felt like a burning passion. "I think," she says, "I was dedicated to following that path. I tried to get into the National Youth Theatre, and didn't, and I tried to get into drama school, and didn't, and then I went to university and was really delighted that I went there. I think having the word 'no' can be quite creative." And then she laughs. "That's the complete opposite to what I said before, that the phone hasn't rung, but I survived. Oh dear," she says with another wild peal of laughter, "what do I mean?"

I'm not quite sure what she means, but I'm getting a sense that she has a slight tendency to preach. Her view that "being disappointed" is "just being unappointed, because I've appointed myself, I've decided how things are going to be" reminds me of linguistically ingenious lessons from the pulpit from evangelical vicars during my own born-again adolescence. But at least her little homilies are delivered with grace, and self-deprecating humour. She has, for example, been playing Debbie from The Archers for 18 years, but she still, she says, "feels like a person who's a bit rubbish". Surely she's being disingenuous? Greig looks agonised. "I'm not. I'm really not. I have a shallow understanding of what it means to be alive, and I know certain things about parenting, and being a wife, and doing the school run. I know little bits, but I'm really a paddler on a beach."

In terms of comedy, too, for which she has won several awards, she claims to be "in the shallows". "I can do a little bit of comedy," she says, "I can be in an in-between place, where I can do a little bit. I'm not Lee Evans, and maybe it's too pastel, because people can't say exactly what colour it is, but maybe it's just a colour you can't describe. When I was asked to play Edith Frank in [the BBC adaptation of] The Diary of Anne Frank, I felt so honoured. That woman was just such a heart-breaking, heart-broken woman."

Her sincerity is touching, actually, and so is her modesty. It makes me think that maybe her comments about her sad horse/puffin face aren't just flashes of please-like-me English humour. When her Beatrice strutted onto the stage at the RSC, voluptuous in tight corset and padded bottom, the critics talked about her "surprise" incarnation as a sex goddess. I think, I say, I'd have been slightly pissed off by that "surprise". Was she? Another peal of laughter. "I think I'm a bit odd," says Greig. "I only read one review, by Charles Spencer in the Telegraph, and I got to the first paragraph, which said 'not exactly beautiful, more like Edwina Currie', which I thought was hilarious." But didn't it upset her? "I suppose we all sort of want to be beautiful," she says, "but when you're not a beauty... Well, we can be beautiful in so many ways, can't we?"

Yes, we can, and actually I think Tamsin Greig is rather beautiful in lots of ways. She's extremely attractive, in the flesh, for a start. She's a bloody good actor. She's modest and she's sweet. She's also rather serious in a profession that's often a bit uncomfortable with serious. What she isn't, I think, is Plato, but who said an actor had to be Plato?

"I don't," she says, when the stage manager comes to march her off, "know if any of that was interesting or helpful? Please," she adds, and it sounds like a joke, but I'm not sure it is one, "don't be a bitch."

'The Little Dog Laughed' opens at the Garrick Theatre, London WC2 on 9 January (Garrick-theatre.co.uk)