Prostitute Caroline Martin described their liaisons, and one incident of drug taking, in an interview with the News of the World.
Deayton, who has a baby with long-term partner Lise Meyer, was reportedly unaware that the 29-year-old was a prostitute.
Publicist Matthew Freud told BBC News Online his client dreads filming Friday's edition of the satirical news quiz.
"He's expecting a pretty rough ride," Mr Freud said, adding that Deayton's mood was "remorseful".
"I think he got properly set up and he obviously feels a bit of a fool."
The BBC said Friday's programme would go ahead as usual, calling the revelations "a personal matter".
Cocaine
Deayton has hosted the programme, alongside regular team captains Ian Hislop and Paul Merton, since it began in 1990. It is now in its 23rd series.
He has become well known for poking fun at celebrities who find themselves at the centre of scandals.
Deayton and Ms Martin exchanged phone numbers after meeting in a Manchester bar five weeks ago, according to the News of the World report.
They were said to have met up twice after that - once at Manchester's Malmaison hotel and again at the Hilton in London.
Ms Martin claimed Deayton took cocaine in front of her at the Hilton.
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