It's hard to imagine a more toxic political combination: a demoralised police force, smarting over a highly critical review of pay and conditions, battered by revelations at the Leveson inquiry, and grieving over the murders of two officers in a horrific gun and grenade attack. Enter a posh Tory MP on his bicycle, treating the police officers on duty in Downing Street as if they were the hired help.

Andrew Mitchell, the Conservative chief whip, admits he was rude, but denies using the words "moron" and "fucking plebs". The two officers stand by their story, which is all the more damaging because it fits into the narrative of a Cabinet stuffed with millionaires who are increasing class divisions. On a visit to Manchester, where he had gone to pay his respects to the local force over the murders of PCs Fiona Bone and Nicola Hughes, the Prime Minister suffered the acute embarrassment of having to disown the conduct of a Cabinet colleague.

No one should underestimate the scale of the rift that has opened up between this government and the police. Rank-and-file officers are furious over the review carried out by Tom Winsor, who takes up a new role next month as the first Chief Inspector of Constabulary having never worked as a police officer. Thirty thousand officers marched through London in protest at the proposals in Winsor's report, which include a lower starting salary and a pay cut for those on "restricted duties" for more than a year.

In London, the force has lived through two years of robust criticism, leading to the resignation of a commissioner. Suddenly, the political party seen as a traditional ally of the police has become an object of loathing. Photographs of Mitchell pushing his bike, wearing a suit and an unfortunate smirk, have become a focus of discontent. His position is all the more difficult because he is so unlike his father, Sir David Mitchell, an amiable wine merchant and former Conservative MP.

Whether the younger Mitchell was known by the nickname "Thrasher" when he was at Rugby is unclear, but at prep school he was known by the unflattering soubriquet "Mitchellsnob". A couple of years as Secretary of State for International Development has not endeared him to right-wing Tories, who loathe the Government's decision to protect the overseas aid budget from cuts in public spending. It's not surprising that police unions have seized the opportunity to strike back, in a week when the dangers of the job have been brought home by the murders in Manchester.

Yet the fact remains that the police have been heavily criticised for both recent and historic failures, including their response to last year's riots, their failure to investigate phone hacking and their handling of the Hillsborough disaster. Of course, Andrew Mitchell should have resigned two days ago, but the snobbish outburst of a Tory Cabinet minister shouldn't prevent a debate about policing in this country.

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