David Cameron has been accused of presiding over a "cover-up" over Conservative Chief Whip Andrew Mitchell's altercation with a Downing Street police officer.

After No 10 ruled out an official inquiry into the encounter, shadow home secretary Yvette Cooper said the Prime Minister appeared determined to prevent the truth coming out.

Pressure on Mr Mitchell intensified after The Daily Telegraph published the full 442-word police log of the incident, which showed he called officers "plebs" and swore at them repeatedly. While he has apologised for showing a lack of respect to the police, Mr Mitchell insisted he did not use the words attributed to him - prompting angry complaints from the Police Federation that he was effectively accusing the officers involved of lying.

The Cabinet Secretary Sir Jeremy Heywood has attempted to draw a line under the matter, arguing that there was no purpose in holding an inquiry as the officer concerned had accepted Mr Mitchell's apology and did not wish to pursue the matter.

However Ms Cooper said that it was essential to establish who was telling the truth, telling ITV's Daybreak: "It now looks like there is a cover-up going on and really I think both Andrew Mitchell and the prime minister need to tell us exactly what is happening."

"You read these reports and you have got a cabinet minister not just swearing at the police but also sneering at them, calling them plebs, saying they should know their place. I don't think the Prime Minister can just dismiss this and try and sweep this under the carpet."

Home Office Minister James Brokenshire insisted that it was possible that both Mr Mitchell and the officer genuinely had different recollections of what happened, telling Sky News: "I have got no reason to doubt the recollections of either Andrew Mitchell or the police officer concerned. It may well be that they can both honestly believe that their recollection of those events is as has been recorded."

Meanwhile, Boris Johnson said it would have been common sense for police to have arrested Mr Mitchell after his tirade against officers in Downing Street. The Mayor of London, who has previously stated that anyone who swears at police should face arrest, said: "If I read the papers correctly there was a proposal to arrest Mr Mitchell for what he said. That seems to be wholly common-sensical. The public order act does allow for police officers' discretion in this matter. They've obviously decided not to go ahead with it. But it shows the gravity of this offence."

Meanwhile, one of Britain's most senior police officers said Mr Mitchell should keep his job, saying "we need to move on". Sir Hugh Orde, president of the Association of Chief Police Officers, said he backed Met Commissioner Bernard Hogan-Howe's view that there was no need for further action.

"There are far more important issues in policing that need to be dealt with and we need to move on from it," Sir Hugh said, adding that the officer involved had "exercised his discretion" in the way that officers did every day of the week in difficult circumstances.