Labour sought to step up the pressure on the beleaguered Liberal Democrat Cabinet minister, urging Mr Cameron to set up an inquiry to establish the truth of the claims surrounding the eight-year-old speeding offence.
Mr Huhne is due to be interviewed this week by Essex Police over the allegations, which first surfaced two weeks ago when his ex-wife, Vicky Pryce, said he had asked someone else to take the penalty points. Subsequent press reports said that she was the person concerned.
Although Mr Huhne has denied the allegations - which date back to his days as an MEP - he has had to endure a steady stream of disclosures apparently supporting Ms Pryce's claims. After one Sunday paper yesterday published details of Ms Pryce's driving licence showing she received three points for an offence on the date concerned, shadow cabinet office minister Tessa Jowell said Mr Cameron had to resolve the issue.
"He should be getting a proper investigation independently - Cabinet Office or wherever - to establish what the facts were and in the light of the facts decide the best course of action," she said.
Downing Street has said that Mr Huhne still has Mr Cameron's "full confidence", but public support for the Energy Secretary has been only lukewarm.
Foreign Secretary William Hague said the police investigation should be allowed to run its course. But asked whether Mr Huhne should stand down from the government in order to clear his name, he said that was not up to him to decide.
"In the media those things are being questioned, but the police are looking into it and so what can we do? We have to let that process take place," he said. "It's his decision."
A photograph of Ms Pryce's licence published yesterday shows a single, three-point fixed penalty offence for speeding on 12 March, 2003 - the date Mr Huhne's car is alleged to have been caught by a speed camera.
Mr Huhne has denied claims that he was actually driving and that Ms Pryce admitted the offence on his behalf as he faced a driving ban if he collected any more penalty points.
It is alleged that he was returning from Stansted Airport to his home in Clapham, south London, having flown in from Strasbourg where the European Parliament sits.
Ms Pryce's licence is marked with the court code 1629, which, the newspaper said, shows that the offence was dealt with by Southend Magistrates' Court in Essex which covers the road network between Stansted and London.
The licence does not show the time of day the offence occurred. However, it is reported that Ms Pryce spent much of the day in central London, attending a conference in the morning and an event at the London School of Economics where she stayed for a dinner until after 10pm.