Energy Secretary Chris Huhne last night faced fresh questions about claims that he persuaded someone else to take speeding points in order to avoid a driving ban. Two newspapers claimed he was involved in a cover-up.

The Sunday Times and The Mail on Sunday published excerpts from an alleged telephone call between Mr Huhne and the person who is said to have taken the points. The offence is said to have occurred in Essex in 2003 when Mr Huhne was still an MEP.

According to the The Mail on Sunday Mr Huhne warned the other person during the call not to let "the genie" out of the bottle by revealing details of what happened. "'There is no evidence for this story unless you give it some legs by saying something. The last thing you want is a half-baked story saying you've taken points for me," Mr Huhne said, according to The MoS. "The only way they can stand that up is by getting you to talk... there is simply no other person who could possibly tell them whether it is true or not."

Mr Huhne allegedly made a reference to the claims being untrue: "There's no question of it coming out, because it's simply not true, that's it."

Last week The Sunday Times published an interview with Mr Huhne's estranged wife, Vicky Pryce, in which she claimed he had asked someone to accept points for him. Today, it also published excerpts from the taped conversation, in which Mr Huhne allegedly told the other person: "If I were you... do not talk. I would have thought you would not want to talk."

The Sunday Times also said Labour MP Simon Danczuk had complained to Essex police in relation to the allegations.

The revelations will heap pressure on Mr Huhne, who until a week ago was seen by many as positioning himself for a challenge to Nick Clegg for the Lib Dem leadership. He twice stood – and was defeated – for the top job before forming part of the negotiating team which struck the power-sharing deal with the Tories last year.