Andrew Mitchell will attempt to rescue his cabinet career by meeting police officers today as he tries to draw a line under his expletive-fuelled rant at the gates of Downing Street.

The chief whip has admitted swearing at the officers who guard the prime minister's residence, but has denied calling them "plebs". 

The class-based insult is toxic for a party trying to shake off its image as being led by out of touch "posh boys".

A YouGov poll published on Friday showed 50% of public think the row shows that Tory MPs see themselves as better than ordinary people.

The survey revealed that 60% of the public believe the outburst "showed his true feelings" and 50% think his behaviour and attitudes reflect those of other Conservative MPs.

Cabinet ministers are said to be openly discussing how to make him quit and a Tory MP said Mitchell now had "no authority at all" while the Daily Telegraph branded him a "laughing stock".

Ian Edwards, the chair of the West Midlands Police Federation, told The Huffington Post UK that officers were "very upset by him saying the officers' accounts aren't true".

The official police account records Mitchell as saying: "Best you learn your f******* place... you don't run this f****** government... You're f****** plebs."

Mitchell chose to dodge this week's Conservative Party conference in Birmingham, his own city, so as to avoid being a "distraction", but will meet police officers at 5pm today.

But his absence did not stop protesters picketing the entrance to the gathering in "I'm A Pleb" t-shirts or prevent him from being the main topic of gossip.

A senior government source told the Daily Mail: "If I were him I would be resigning, but then he is not a normal individual."

George Eustice, the Tory MP who used to be David Cameron's press secretary and also ran media operations at Conservative Central Office before being elected, told a conference fringe meeting that the Tory's posh image was a "major problem" and suggested Mitchell's "unforced" rant had not helped.

And the BBC's Andrew Neil questioned whether Mitchell was a "dead man walking", tweeting: "Cabinet ministers openly talking with each other about how to persuade him to quit".

Mitchell does not appear to be willing to surrender his cabinet position and the Daily Telegraph reports that friends of the embattled Sutton Coldfield MP have even commissioned focus groups to see if they can prove to the prime minister that voters do not care about the scandal.

The role of the chief whip is to enforce party discipline, to avoid MPs embarrassing the government. Quite hard to do if your cabinet colleagues are openly making jokes about you. On the suggestion Mitchell could be made High Commissioner to Rwanda, Iain Duncan Smith replied: “I hear there are no gates in Rwanda”.

And an unnamed Tory MP told the Evening Standard: “He should have been fired straight away and Lord alone knows why the PM let him stay on. It was not only a political disaster for us but we now have a chief whip who has no authority at all."

In a further blow for Mitchell, the Daily Telegraph took the unusual step of urging the prime minister to fire him.

"The chief whip is now a laughing stock and a walking, talking embodiment of everything with which David Cameron would least like his party to be associated," the paper declared in an editorial today.

Mitchell is also being targeted for his decision in his last days as international development secretary to restore aid to Rwanda, despite concerns over the human rights record of president Paul Kagame. His replacement at DfiD, Justine Greening, is reported to be considering reversing that decision.