For five of the show's 11 years, she tottered around the Boston bar acting like a bossy prefect on library duty, straining to bring a little intellectual light to the lives of the bozo barflies, and wrestling with her chauvinistic suitor, the terminally dumb Sam, played by Ted Danson.
"I think Ted and I only had one argument in my five years," Long says. "We would have done better had we been more verbal with each other about some of the things that were going on. It was all fun, though.
"But when Nick Colasanto, who played Coach, passed away, Diane and I missed him greatly. Woody Harrelson is wonderful, but there was something missing for me without Coach. Once he was gone, Diane had nobody to turn to when the crowd ganged up on her. In any case, I didn't want to be stuck in that part for the rest of my life."
She sits sipping tea, with her perfectly pressed suit and her perfectly pressed smile and hair that bounces with an almost audible "boing" whenever she turns her head. As she tells you she was kidnapped as a baby, you think it sounds like a typically melodramatic Diane story. But it isn't. It's a joke.
"Well, you would think I had been kidnapped!" she laughs. "Nobody could have come from a less theatrical family than I did. Here were my parents, both teachers, and they had this hammy kid who always went for schtick and jokes and goofy stuff. I'd always been mimicking and imitating, and it was something I'd never had a chance to do until I was offered this."
"This" is what Long is here to promote - The Brady Bunch Movie - and the reason she has left her sunny Los Angeles home for the London fug. The new film is a big-screen reworking of the kitsch sitcom about a terminally jolly family who symbolise a wholesome America that never was, except perhaps in the dreams of Michael Medved.
But there's a pleasant surprise - the film is a hoot. Admittedly, much of the humour might lack that extra resonance for anyone who didn't catch the series. If so, you'll just have to take it from a fan - reproduction of sets, costumes, voices and mannerisms of the original cast is impeccable. The comedy has a new tang, with the Bradys living 1970s lives and wearing 1970s fabrics in polluted, crime-ridden, post-Reagan America. There might not be another film this year so gloriously dotty.
Long plays Carol Brady, the mother. Or rather, she plays Florence Henderson playing Carol Brady, Henderson being the actress who originally immortalised the ever-smiling Stepfordesque housewife.
"We all had very specific assignments," Long reveals, "because we were playing people whose every detail was recognisable to a large chunk of the audience. I prepared by watching the tapes, then recording them on an audio cassette so I could really study Florence's voice.
"That was very tough for me, and quite restrictive. At first, it felt like a suit of uncomfortable clothes - too tight and maybe from the wrong fabric. It was certainly the most technical role I've had, but once I'd mastered those things, I could bring in something of myself."
Given Long's extraordinary brightness and vivacity, and her wonderful comic timing, it's peculiar that she has never found a movie to do her justice. After joining the resident company of Second City, Chicago's much-admired improvisational group, it seemed things were taking off. She walked from Second City straight into A Small Circle of Friends, a film about anti-war demonstrations, and was spotted by Steven Spielberg, who wanted her for a major part in his next film. Instead, she plumped for a prehistoric comedy called Caveman. Ringo Starr and his wife Barbara Bach took the leads. It was not a success.
"I lost that film with Steven because of Caveman," she shrugs. She won't name the movie, but given it was 1980, she must have been in line for Raiders of the Lost Ark or ET.
"I don't regret doing Caveman. When I read the script, I thought it was charming, only it didn't turn out quite as well as I could have imagined, but it's silly and funny so..." She trails off. Her talent is not in doubt - along with Dianne Wiest, who has only recently found her niche, she is one of the most amiable and inventive comic actresses in Hollywood. But her script choice has never been as dependable as her performances.
Much of this is down to timing. "I got the script for the first Cheers when I was working on the movie Night Shift and I thought, 'This is really good.' I had to decide whether I was willing to commit five years of my life on the basis of one script."
She won't admit to mistakes. "I think other people made mistakes," she says instead, alluding to the second role she lost, in the mid-1980s. "I was pregnant," she recalls, "and I had told the studio that the doctors said I was young enough to recover very quickly. It wasn't their lack of confidence that lost me the role. I think they were just looking for a new star."
She stops for a moment and thinks. "I can't tell you who got the part," she says. "The film was not a success, but the actress was. I think I would have been much better. But you can over-think these things, you know."
She doesn't sound bitter, just resigned. Deep down, you suspect she knows what everybody knows about Shelley Long - terrific comedienne, never quite found the right film. She came closest in the underrated 1984 comedy-drama Irreconcilable Differences, in which she and screen husband Ryan O'Neal were divorced by their daughter Drew Barrymore. Without the forbidding title, it might have been a bigger hit.
"I'm very proud of that one," she smiles. "I'd like to do more like that. But it is still so difficult for ladies in Hollywood to get the roles they want. That might change if, God willing, romantic comedies continue to flourish. But those sorts of films are rare, and the chances of them succeeding are not as great as some of the more sensational pictures."
You can't help feeling that her latest film, a remake of the Disney comedy Freaky Friday, in which a mother and daughter swap bodies, is something of a step backwards. If every performer really does have a role they were born to play, such digressions must, for Long, only push that role further out of reach.
"I enjoyed playing the daughter more than the mother," she says, letting out an infectious, resounding guffaw. "I had to learn to rollerblade. The tricky part is stopping. It's all great fun until you have to stop, and then it's aaaarrrrgghh!" Diane Chambers might take that as some kind of metaphor. But then, you can over-think these things, you know.
n 'The Brady Bunch Movie' is on release from Friday