Less than 24 hours later, a hurricane tore across the south coast of England in a four-hour frenzy that killed 19 people, ripped up 15 million trees and caused billions of pounds worth of damage.
But on a programme about the night of 15 October, Mr Fish, who is affectionately known as "Mr Polyester" because of his striking taste in suits, now claims that he never said there would not be a hurricane. On Storm of the Century, to be broadcast on Radio 2 tonight, Mr Fish says it was the media that got it wrong.
"The woman referred to was talking about a potential hurricane in Florida that had been mentioned in the news. The Met Office got it spectacularly wrong, but I was only one of the messengers," he says in the interview. Bearing in mind the number of times the television clip has been replayed, this would be a tough argument to win at the best of times. The footage is currently being shown to flag a television programme about the storm. But Mr Fish has another problem - his Nemesis, in the shape of the person behind that fateful telephone call, has also come back to haunt him.
The woman who made the call is Anita Hart, 46, from north-west London. It was her son, Gaon, who, while doing meteorology as part of a geography degree, compiled the weather forecast that prompted Mrs Hart's call.
In a "join-the-dots" weather prediction, of a kind he often made for his parents, he had warned them not to go on a planned caravan trip to Wales after seeing what looked like a severe storm approaching. They reacted with disbelief, thinking that anything so serious would surely have been noted elsewhere, and decided to call the BBC. Hence the fateful call, he says, to Michael Fish.
Mrs Hart is currently travelling and could not comment yesterday. But Gaon Hart, now a lawyer, said the pair were astonished to hear of Mr Fish's denial.
"My mother actually spoke to Michael Fish because she called the BBC and was accidentally put through to him. She never mentioned anything about Florida, and nor did he when the forecast went out," Mr Hart, 31, said yesterday.
"It's coincidental indeed that he happens to get a phone call about one hurricane and another in Florida on the same day," he observed. "It just doesn't add up." His mother, he said, had even become an answer to a Trivial Pursuit question, in an American version of the game. All things considered, he could find little explanation for why Mr Fish had suddenly decided to speak out.
"I think he's realised that it's going to haunt him for the rest of his days. I don't want to be nasty - perhaps he legitimately doesn't remember ... But it's on the record and it did happen." Mr Hart said that neither he nor his mother wished Mr Fish any ill-will, despite the obvious disparities between what they and the weatherman say happened.
"My mum's going to find it amusing. She finds it all very amusing. In fact, she feels sorry for him."
Whatever the truth, there is one possible explanation for Mr Fish's apparent keenness to separate his professional image from those notorious quotes. In June it was reported that the weatherman had been recruited by Florida meteorologists to help spot hurricanes threatening Miami. He was said to be part of a new "co-operation pact" between the Meteorological Office in Bracknell, Berkshire, and the Florida authorities, which are keen to deploy both British supercomputers and staff expertise.
Michael Fish could not be reached to comment last night.