Eventually, she took the project to Channel 5, who were not so fazed. "They say that's just the point," she maintains. "Look at Jack Docherty - he was undoubtedly a good interviewer, but he wasn't high-profile."
Channel 5 may well be rewarded for their scant regard for the fame-ometer, because Banks is certainly a talented performer. She plays with consummate ease everything from a superannuated Russian prima ballerina to a Barbie Doll-esque American shopping channel presenter.
Her most celebrated creation, however, remains the little girl with the warped sense of wisdom she first developed on the superior Channel 4 sketch show, Absolutely, a few years ago. She appears in every episode of the new 13-part series. In one, she delivers her considered opinion of Liam Gallagher - "He just wants to do drinking beer, buying houses and smelling talcum powder".
Banks reckons the little girl is popular because she's direct. People ask me, 'Do you watch children a lot?' The answer is no, it's just what I remember from my own childhood. I often think, 'Does anybody share this view?', but by the response I get to the little girl, people must think a bit the same as me."
If there's a theme running through the characters, Banks muses, it's that "they're all messed-up women. The show is all about my fears - the women are all different aspects of people I could turn out to be. I don't use a lot of devices and I don't believe in plundering other people's lives - only my own."
The show bustles along at a fair old pace. "In a sketch show, you've just got to keep on moving," Banks observes. "Sketch comedy is better shorter, like The Fast Show - they're really smart."
Another similarity with the Paul Whitehouse/Charlie Higson vehicle is Banks's reliance on verbal and visual catchphrases. "It's like playground humour," she explains. "Shared humour is a good point of contact."
Although by her own admission not in the first division of fame, Banks has still managed to clock up a pretty impressive CV. Her best-known work has been Absolutely, which she worked on between 1989 and 1993 with comedians such as Docherty and Gordon Kennedy (who also appears in the new series). "We were similar to The Fast Show, but very untrendy," Banks recalls. "Sketch comedy was then seen as a post-Oxbridge domain. Then Vic and Bob came along and put a different spin on it. They made soundbite comedy acceptable."
Absolutely was absolutely terminated when "Channel 4 demanded a higher profile for its performers," Banks recounts. "They wanted to elect one of us to be the star and appear on the front cover of magazines. We were pleased to have got to that stage without doing any publicity. So it was a sticky moment."
Banks has also appeared for several months in the West End run of An Evening With Gary Lineker opposite Caroline Quentin, and on Saturday Night Live and Dream On in the States. She had offers to stay on in LA, but wisely turned them down. "I'm not young or beautiful or any of the things you need to be in Hollywood," she smiles. Instead, she returned home where she has built up a healthy second career as a producer on such programmes as The Jack Docherty Show and Armstrong and Miller.
In between times, the Cambridge-educated Banks somehow managed to fit in co-writing, with Amanda Swift, The Joke's On Us, a book about women in comedy. She is uncomfortable, however, about being saddled with the role of spokesperson for female comics. "The book is a bit of a crusty read," she concedes, "and inadvertently it has become ghettoising. All I wanted to do was just be funny, and all the time I was being asked to give historical analyses of why there are so few women comedians. That's not an issue I want to discuss. The proof of it is in what you see. French and Saunders, Caroline Aherne and Victoria Wood are all proving it by doing it. I'd rather be doing that."
Bearing in mind the unhappy experiences of Emma Thompson and Josie Lawrence with their one-woman TV shows, Banks is wary of making bold predictions. "I'm not looking for a big break," she claims. "I know I'm not prime-time. I just hope it doesn't bomb. If it does, I'm looking down the barrel of a lot of producing work in the coming years."
The Morwenna Banks Show is on Tuesdays at 9.55pm on C5