The story gets fishier...
A couple of paragraphs from Wikipedia's Article on Michael Fish:
Fish said in a BBC interview that there was actually no woman caller who phoned in to the BBC regarding the storm (although over the years many have claimed to be the woman caller). It was in fact a white lie he made up himself, as another staff member at the BBC told him his mother in Wales was going to Florida and mentioned she had heard there was a storm coming, so he thought it would be a good opening line to start the forecast with, and said "Earlier on today, apparently, a woman rang the BBC..."
...In later years, Fish claimed that he had been referring to that year's Atlantic Hurricane Floyd affecting the Florida Keys at the time, in a link to a news story in the BBC One O'Clock News that preceded the weather bulletin. But he did not mention Florida in his forecast, which was made amid widespread worries about a coming storm: that morning, the Surrey Mirror had warned of "furious gales", so both his caller and his viewers likely believed he was referring to Britain. Fish did go on to warn of high winds for the UK, although the storm that actually occurred was far stronger than he had predicted (albeit, technically not a hurricane).