Jamie Theakston presents TV and radio shows
Theakston, best-known for presenting children's and music TV shows, has said he was tricked into visiting a vice club and then blackmailed after being photographed.
He has admitted becoming involved with the prostitute in London after a Christmas party, but said things "went too far" and that he found the publicity in tabloid newspapers "extremely embarrassing".
"It was one night before Christmas that went too far.
"As someone who values their privacy it is extremely embarrassing and I would like to apologise to my close friends and family."
Theakston attempted to block the revelations in the Sunday People newspaper through a court injunction, the paper said, but a judge rejected his appeal for privacy.
The newspaper says he engaged in "sex games" with a prostitute in a dungeon-style room in a brothel in London's high-class Mayfair area.
'Drunk'
But talking to another newspaper, the News of the World, Theakston says he was asked by an unlicensed minicab driver whether he wanted to go to a late-night drinking venue.
"I thought, 'Why not? It's Christmas'. I must have been so totally drunk I told him to take me there," he said, according to the paper.
A girl began to do a striptease dance for him and invited him into a private room, where she performed a "sex act" on him, he said.
He returned after realising that his mobile phone was missing, but nobody admitted to knowing anything about it or the photos when he asked, he said.
When he got a new phone with the same number, he began receiving text and voicemail messages demanding money.
"I know it was foolish for me to get into this situation in the first place but I'm not married," he told the News of the World.
"I'm a single guy, I haven't broken the law. You just have to stand up to these people.
"I've never done anything like this in the past and I'll certainly never do anything like it again."
Theakston is a former presenter of children's TV show Live and Kicking and currently presents Top of the Pops and a Saturday radio show on BBC Radio 1.
He split from actress Joely Richardson last year, although the pair remained close.
A BBC spokesman said: "As far as we're concerned, it is a personal thing."
Police said they had not received a formal complaint about the blackmail allegations.
"Any complaint received would be fully and thoroughly investigated," a Scotland Yard spokesman said.