More than a week after the story first surfaced in the press, Mr Huhne finally broke his silence to insist that the allegations, which date back to 2003, were "simply incorrect".
He was forced to speak out after Essex Police disclosed that they were considering whether to launch a criminal investigation in response to a formal complaint by the Labour MP Simon Danczuk.
"All I want to say is that these allegations are simply incorrect," Mr Huhne said.
"They've been made before and they've been shown to be untrue, and I very much welcome the referral to the police as it will draw a line under the matter.
"I don't want to say anything more than that, I think the police can get to the bottom of this."
Earlier, No 10 had been forced to take the unusual step of saying that Mr Huhne denied all the allegations against him, after the Liberal Democrat minister had refused to comment on the story.
Asked at the morning briefing for political journalists whether Mr Cameron had full confidence in Mr Huhne, the Prime Minister's spokesman said: "Yes, he does."
The spokesman also indicated that even if police did launch an investigation, Mr Huhne could retain his Cabinet post while it was carried out.
"It has certainly happened in the past," the spokesman said.
The latest developments left Mr Huhne looking uncomfortably reliant on the Prime Minister's support, just two weeks after he angrily confronted Mr Cameron in Cabinet over the tactics of the No campaign in the AV referendum.
His move was widely seen as an attempt to position himself as a potential rival to Nick Clegg.