At the root of the trouble is Dropping Names, a memoir by the writer David Benedictus, which alleges that during the 1980s, Fish "was in The News of the World as being part of a wife-swapping circle in East Twickenham."
It's a shocking claim, but evidence to back it up is thin on the ground. Pandora can find no record of any such NOTW article, and Benedictus now admits that he "didn't check the details when writing the memoir."
All of which left Fish yesterday considering how best to respond to the allegation. "There is no truth in it," he told me. "As to what I might do, I will need time to seek advice and find out more information. I have never heard of a David Benedictus ... I have just checked his website and I have never met or seen him in my life."
Benedictus reckons otherwise. As I noted last week, his book claims they exchanged unneighbourly words when his dog, Magpie, "squatted down on (Fish's) nasty little rosebush, in the middle of his nasty little lawn."
Pressed on the wife-swapping allegation, Benedictus tells me: "I believe there was an article claiming that, but I didn't check the references for my memoir."
* Strangely, for a pioneer of reality TV, pop poppet Myleene Klass has more upstairs than we previously believed.
To stave off boredom during her forthcoming UK tour, Klass has enrolled on an Open University degree course in - of all things - astronomy.
"I don't have time, with all the concerts and travel I have to do, to sit in a university, so I am doing a correspondence course," she tells me.
"I send in essays and work and they send it back. So my tour bus is loaded with books, which isn't exactly very rock'n'roll."
Maybe not, but Klass - speaking at Sunday's Veuve Cliquot polo Gold Cup - has an impressive mentor.
"Professor Colin Pillinger, the Beagle man, is a friend and is giving me some private tutorials," she adds, excitedly.
"I can't wait. I'd like to be able to use this knowledge to go and make science programmes for TV. Like Carol Vorderman, but for a younger generation."
* Sharon Stone is much in evidence in London, where she's filming the sequel to Basic Instinct. A host of stars - from Stan Collymore to Charlotte Rampling - feature in the flick, but it isn't everyone's cup of tea.
The French supermodel Sarah Marshall was asked to play a cousin (and lover) of the film's iconic heroine, right, but turned down the role in order to avoid being typecast.
Says socialite Andy Wong, with whom Marshall attended Sunday's Veuve Cliquot Gold Cup: "Sarah didn't want to be thought of as a lesbian actress for the rest of her career."
Here's hoping. Back in France, Marshall's stormy relationship with ex-husband Alexandre Anthony - a bisexual actor whom she divorced last month - is a gossip-column staple.
* Biting her lip, Margaret Thatcher marked the passing of Sir Edward Heath with a sombre press statement, dubbing her bête noir "a political giant."
Other foes were less dignified. The UK Independence Party carried two polls on its website, headlined "Heath kicks the bucket". One asked: "Was Heath a traitor?" (84 per cent said yes). The other: "Will you miss Heath?" (91 per cent said no).
Beneath an obituary too nasty to bear repetition, UKIP's site flags a date for the diary: the party's Woking branch is holding a dinner-dance to celebrate the fact that "Ted is brown bread".
As to the former PM's funeral: "I will attend his last goodbye wearing the biggest UKIP rosette I can find," writes one correspondent. " I'll also stick one atop a pole and wave it at the cortege."
* The Queen champions British explorers, no matter what frontier they push. Tomorrow, the comedian Tim FitzHigham will dine at Buckingham Palace, having - God willing - rowed up the Thames in a bathtub.
Speaking from Margate yesterday, the intrepid FitzHigham said he's named the Thomas Crapper bathtub Lilibet II, in Her Majesty's honour.
"Two years ago, I rowed a paper boat 160 miles down the Thames, and she wrote to congratulate me," he said. "This time, I row all the way upriver to Tower Bridge. It's in aid of Comic Relief, and the Queen's written again, to wish me luck."
There is but one problem. "Tim is panicking, because the only suit he owns is covered in horse manure," adds his agent. "I've told him not to bother cleaning it, though: the Royals love a bit of horseshit."Reuse content