Not that this self-effacing 39-year-old would say so herself. "I hate people who pointlessly put themselves down," she says, but it soon becomes clear that Davis is far too honest and self-critical to make grandiose claims. She even admits she's not very sure whether the second series of Nighty Night is any good. "I certainly don't think it's better than the first series," she says. "I'll be happy if it's as good as, but I'm fearful that it's worse. But that is very much my nature."
Nighty Night, for the uninitiated - and that probably includes most people - is a gleefully dark sitcom (a "sick-com", Davis dubs it) about an evil suburban hairdresser called Jill (played by Davis), who, discovering that her husband, Terry (played by Kevin Eldon), is ill, starts to tell people that he's dying of cancer. Meanwhile, she meddles in the marriage of her MS-suffering neighbour, Cath (played by Rebecca Front), and husband Don - played by Angus Deayton, in a role that may help to restore his credibility. In the final episode of series one, Jill married Glenn (Mark Gatiss from The League of Gentlemen), while bumping off several of the characters - Davis claims she can't remember which. But with a chutzpah that would have embarrassed even Dallas scriptwriters, she has resurrected the lot of them, and relocated their "shenanigans" to Cornwall.
"We needed somewhere seasidey for Cath to recuperate, and Ibiza was suggested, but that's not very Cath," Davis says, although new viewers may not comprehend such nuances of character. "I don't know if you can understand it if you haven't seen the first series. I tried to explain what's been going on, but that's not my strongest point." Is she afraid that bewildered newcomers to Nighty Night will be wondering what all the fuss was about? "I was glad that there wasn't much hype around the first series going out - I hate that pressure and that's what I've been feeling on this one," she says. "The worst fear is that it's just not very funny and that it won't work."
Despite Davis' natural modesty, there seems little fear of that. For a start, she has created such a striking monster in Jill. "I'm not entirely sure where Jill came from," she says. "I knew that I thought a hairdresser was a good idea, but the rest just came from nowhere. I do think there are easily people as evil as Jill around - you know, you read the papers and watch those Tricia-like shows." In fact, Jill bears a certain resemblance to another sacred monster - Beverly, from Mike Leigh's Abigail's Party. "I think that's very true - I mean, not consciously," says Davis. "I didn't think about that until it was pointed out. But Abigail's Party is one of my favourite things. On the whole, though, the dialogue side of Jill seemed to come out quite easily. I really don't know quite what it is."
The idea that Jill is part of Davis' unconscious has titillated many observers, some of whom have analysed it as anger directed at women, while others have discerned a contempt aimed at men. In a recent interview, Davis seemed to be suggesting it was men's sexual simplicity, their easily tweaked "triggers", that allowed Jill to thrive. Davis looks aghast.
"That makes me sound so dismissive, and I don't really feel that way," she says. "The trouble is that I can hold that opinion for half an hour, and then hold a completely contrary one. That same article said I was anti-porn. I'm not anti-porn."
Davis says that Jill's over-the-top sexuality, like an X-rated panto dame, seems to appeals to gay men - and the occasional pervert. "I get the odd letter, usually with scrawly handwriting," she says. "I tend to not respond." On the whole, Davis says that television is a medium that disconnects her from the audience, and so she has no qualms expressing the dark side about her humour. "But I think if I had to sit in front of a board of people and actually explain myself, I'd find that much more difficult," she says. "In the end, though, if you don't find it funny, well, I do. Don't analyse the morals. The weird thing is that in real life I really want to be liked, but in art I don't care."
Ah, yes, in real life. Much has been made of the fact that Davis, born in Bath in 1966, came from a nicely brought-up Baptist background, and that her mother's father and brother were vicars. In one interview, Davis said she'd like to go into a therapy session with her mother and find out what she really thought of Nighty Night. She says: "I did telephone my mother after that article came out, and she said, 'You know how it is, papers misquote', and I said, 'Well, it wasn't exactly a misquote'.
"I don't know how it is with other people, but I don't really sit down with my family and discuss my work or analyse the way I think. I don't know what to say about my mum - I just know that she would be delighted if I wrote something like Where the Heart Is. My dad is very different. We share the same sense of humour. We used to laugh at the same stuff when I was growing up - mostly Fawlty Towers; Monty Python. He took me to see Joe Orton plays, Pinter and stuff - like very young to be taken to those kinds of things. I'm not remotely comparing myself to Harold Pinter, but I just remember phrases like 'chops your spine off' and things that were visually very violent - loving that when I was very young.
"I think it's been overdone this Oranges Are Not the Only Fruit kind of environment, where I was being held down by religious zealots. Despite the fact that my mother probably doesn't like Nighty Night, they do watch a lot of stuff. It's just that my dad is particularly into this stuff. He would watch Chris Morris regardless of whether I was in it."
In fact, it was her father who inspired the title of Nighty Night. Peter Baynham, the comedian behind last year's BBC2 adult animation I Am Not an Animal, is a close friend and has often stayed with the Davis family in Bath. "My dad, who's a very sweet-natured person, used to say 'nighty night', and Pete would always find it hilarious that at my age my dad said that. So he started calling him Nighty Night - 'how's Nighty Night doing?', that sort of thing. I think he suggested calling the show Nighty Night. It's sad really, because now it's got so many evil connotations."
Davis is adamant there won't be a third series. She's got two half-written film ideas and would like to do a sitcom along the lines of Curb Your Enthusiasm. "What I mean is that I like the way that works," she says. "I think they improvise a lot." She says she prefers improvisation to writing, partly a legacy of her years in a Bath theatre troupe - "it was a sort of country version of Who's Line is it Anyway?". In the meantime, there are offers of work, although she now finds herself being typecast. "If I'm sent a script, I was always read the description of the character and it always says 'hard', 'bitch', 'assertive' or whatever," she says. But in a new film, Confetti, a mockumentary co-starring Martin Freeman, Davis plays a marriage counsellor. "But [I'm] also quite nasty, but that's my own fault because it's an improvised film and that's what came out."
She would also like to try her hand at directing, part of the overall control she feels she wants over her material. "I'm massively, obsessively... I won't let things go - even down to the trailers," she says. "Apparently, they're trailing [Nighty Night] at the moment and it's got scenes in it that aren't even in the programme."
In fact, it seems appropriate that we're conducting this interview in an editing suite, away from the usual haunts of the publicity circus. Davis hates having her photograph taken, despite having a ready, radiant smile that punctuates most of her replies. "Yes, but if I smile for photographs, it looks forced, and if I don't then it reinforces that 'evil, dark, depressed woman thing'," she says. "I don't do chat shows - I find it hard to give simple answers. And I don't want to delve into my personal life. That just seems a very odd concept."
In fact, so frustrated was a recent lengthy profile of Davis at not discovering more about her love life, that the writer resorted to quoting a friend who had seen Davis snogging a man in London. "Yes, it did seem odd that," she says. "I'm either seen as a recluse, or a lesbian, or perhaps that I've got some secret love children. I just let people keep on wondering."
'Nighty Night' starts on Tuesday on BBC3