Culture Secretary John Whittingdale has admitted he had a relationship with an escort but said he did not know her real occupation.
He said he ended the relationship as soon as he found out, in February 2014.
BBC political editor Laura Kuenssberg said it raises questions about his role in press regulation, given some papers had the story but did not publish it.
Mr Whittingdale insisted it had not compromised his job as culture, media and sport secretary, from May 2015.
Downing Street said Mr Whittingdale "is a single man entitled to a private life" and had the full confidence of Prime Minister David Cameron.
Mr Whittingdale told BBC Newsnight: "Between August 2013 and February 2014, I had a relationship with someone who I first met through Match.com.
"She was a similar age and lived close to me. At no time did she give me any indication of of her real occupation and I only discovered this when I was made aware that someone was trying to sell a story about me to tabloid newspapers. As soon as I discovered, I ended the relationship.
"This is an old story which was a bit embarrassing at the time. The events occurred long before I took up my present position and it has never had any influence on the decisions I have made as culture secretary."
Labour shadow cabinet minister Chris Bryant, who was shadow culture secretary until September last year, said: "It seems the press were quite deliberately holding a sword of Damocles over John Whittingdale.
"He has a perfect right to a private life but as soon as he knew this he should have withdrawn from all regulation of the press.
Mr Bryant added that the prime minister had promised to fully implement the recommendation of the Leveson Inquiry into press standards, adding: "That's what he should deliver."
Before taking up the cabinet post Mr Whittingdale served as chairman of the Commons Culture, Media and Sport Committee for a decade.
Earlier this month the journalism website Byline reported that Mr Whittingdale had had a relationship with a professional dominatrix and fetish escort.
BBC political correspondent Ben Wright says the fact the story stayed out of the press has raised questions about a potential conflict of interest involving the man in charge of media regulation and the motivation of newspapers and broadcasters not to report it.
A number of newspapers told Newsnight they did not run the story because it was not in the public interest.
However, Brian Cathcart, co-founder of campaign group Hacked Off which wants tougher press regulation, said Mr Whittingdale's credibility had been damaged.