Chief Whip Andrew Mitchell is clinging to his job despite sustained calls for him to be sacked over disputed claims he called police officers "plebs" in a foul-mouthed outburst.

Labour renewed demands on Prime Minister David Cameron to axe him after an attempted "clear the air" meeting with local police representatives ended with them saying his position was "untenable".

But Defence Secretary Philip Hammond rallied to his Cabinet colleague's defence, accusing the Police Federation of trying to "hijack" the row to bring up other issues and grievances with the Government. And a Tory source insisted the meeting had changed nothing, saying Mr Mitchell "fully intends to be at his desk doing the job he is paid to do on Monday morning".

Emerging from Friday night's meeting in the MP's Sutton Coldfield constituency, the chairman of the West Mercia federation Ken Mackaill accused the senior politician of questioning police integrity.

Though he admits swearing when he was refused access through the Downing Street gates on his bicycle, and has apologised personally to the officer involved, Mr Mitchell denies calling the officers who bore the brunt of his outburst "plebs". That is at odds with the officer's written log of the outburst.

"He refused to tell us what he did say on the grounds he did not want to impugn police officers' integrity," Mr Mackaill said following the 45-minute talks with three local federations. "Unfortunately that is exactly what happened: the question of integrity remains unresolved. He is continuing to refuse to elaborate on what happened and I think his position is untenable. I think Mr Mitchell now has no option but to resign."

Shadow home secretary Yvette Cooper said: "David Cameron is the only person left still backing Andrew Mitchell. How long is the Prime Minister going to let this drag on? The drawn out saga of half apology and oblique denial has left a cloud hanging over the Government's attitude to public servants. It is now very hard for the Chief Whip to command respect in Parliament or beyond.

"The Prime Minister needs now to show some leadership and judgment and take seriously the message this incident has sent to people across the country about his Government. He needs to end this now and make Andrew Mitchell stand down as Chief Whip straight away."

However the Tory source said the Prime Minister was "very robust" in his position on not removing Mr Mitchell. Comparing the issue to a road accident where three witnesses all had different accounts of what happened, the source said: "The problem is there is always going to be a difference of opinion about what was said. There are no liars. People just have different recollections. Andrew Mitchell is clear he did not use the word pleb."

Mr Cameron has repeatedly said that the issue is closed as the officer at the centre of the storm has accepted a personal apology from Mr Mitchell and no formal complaint has been made. Senior police chiefs have also called publicly for a line to be drawn under the affair.