The publishers of the Sunday Times dropped their challenge at the High Court in London to an Essex Police bid to obtain emails relating to the Chris Huhne speeding case On Friday.
Times Newspapers Ltd were asking the High Court in London to quash a crown court order requiring production of the emails.
The case concerns emails between Vicky Pryce, Huhne's ex-wife, and Isabel Oakeshott, the Sunday Times political editor.
It follows allegations that the Energy Secretary asked his former wife to take speeding points for him.
On Friday morning a No.10 spokeswoman said : "The Prime Minister has confidence in the Energy Secretary."
It was announced late last year that prosecutors were "very close" to making a decision on whether or not to charge the Energy Secretary.
In September Huhne revealed that Pryce, his wife of 26 years has still not accepted his apology after his affair with a PR adviser ended their marriage in 2010.
Huhne also used the interview to again deny that he asked his wife to accept speeding penalty points on his behalf in 2003, a matter which was then investigation by Essex Police and the Crown Prosecution Service.
"Frankly it was an appalling set of circumstances," Huhne said. "In retrospect I can see that I was running some substantial risks, for example, in what I was doing, politically, as well.
News reports have suggested ministers are on alert for a mini reshuffle if the case spells the end of Huhne's cabinet career. He would be replaced by a Liberal Democrat, and many have tipped foreign office minister Jeremy Browne. Huhne would be third cabinet minister to step down, after David Laws and Liam Fox.
Essex Police obtained a production order to seize the emails at a private hearing last October.
The newspaper then decided to seek judicial review of the police move - leading to the prosecution decision being put on hold.
The police investigation followed claims Pryce made in a Sunday Times interview that Liberal Democrat Huhne had asked "someone" to take points on his behalf in order to avoid losing his licence.
It later emerged that the "someone" was allegedly Pryce.
Police have already obtained an affidavit she signed when she made her allegations to the newspaper, as well as a taped telephone conversation between her and Huhne.
The speeding offence is alleged to have taken place in 2003 when the then-MEP was driving home from Stansted Airport after flying back from the European Parliament.
Huhne, who left Pryce for another woman, has denied the points allegations.