In a letter to the Prime Minister, Mr Mitchell admitted swearing at officers when he told them: “I thought you guys were supposed to f***ing help us”.

However, he continued to strongly deny calling the police “plebs” or “morons” but accepted that he was no longer “able to fulfil my duties”.

The announcement came a month after the chief whip was involved in an angry confrontation with Downing Street police officers which has led to him being openly mocked by his colleagues.

Mr Mitchell’s departure from the Government will spark a mini reshuffle – just weeks after Mr Cameron promoted Mr Mitchell in a shake-up of the Cabinet in September. It threatens to call into question the Prime Minister’s judgement in staunchly defending Mr Mitchell for several weeks.

The chief whip, who is responsible for enforcing Conservative Party discipline in the Commons, is understood to have considered his position after being openly criticised at a meeting of Conservative MPs on Wednesday evening.

Mr Mitchell’s deputy, John Randall, is said to have threatened to resign earlier this week over the issue.

Mr Mitchell waited for David Cameron to return from Brussels last night before resigning in a face-to-face meeting at Chequers, the Prime Minister’s official country residence.

In his resignation letter to the Prime Minister, Mr Mitchell said: “Over the last two days it has become clear to me that whatever the rights and wrongs of the matter I will not be able to fulfil my duties as we would both wish. Nor is it fair to continue to put my family and colleagues through this upsetting and damaging publicity.”

The resignation calls into question Mr Cameron’s decision to publicly and repeatedly defend Mr Mitchell for several weeks after details of his outburst were leaked.

Senior ministers had privately concluded last month that the chief whip’s position was untenable as his confrontation continued to overshadow the Government’s political agenda.

In his letter accepting the chief whip’s resignation, Mr Cameron accepted that the resignation was now “necessary”.

“I regret that this has become necessary, and am very grateful for all you have done, both in Government and in Opposition,” he said. “As you have acknowledged, the incident in Downing Street was not acceptable and you were right to apologise for it.”

The incident which sparked Mr Mitchell’s resignation occurred on Wednesday September 19th, when he was attempting to cycle out of Downing Street.

An official police record of the incident, subsequently leaked to The Daily Telegraph, showed that he refused to comply with police officers, angrily swore at them and was then threatened with arrest after he called them “plebs”

The police log stated that officers had asked Mr Mitchell to dismount from his bicycle and wheel it through a pedestrian exit. However, the log then said: “There were several members of public present as is the norm opposite the pedestrian gate and as we neared it, Mr Mitchell said: ‘Best you learn your f—— place…you don’t run this f—— government …you’re f—— plebs.’”

The officer noted that members of the public looked “visibly shocked” by Mr Mitchell’s language and the Chief Whip was warned that he if he continued to swear he would be arrested under the Public Order Act.

The police record notes: “Mr Mitchell was then silent and left saying ‘you haven’t heard the last of this’ as he cycled off.”

In his resignation letter to Mr Cameron, the chief whip gave his most fulsome explanation of his version of events.

He said: “I have made clear to you – and I give you my categorical assurance again – that I did not never have and never would call a police officer a ‘pleb’ or a ‘moron’ or used any of the other pejorative descriptions attributed to me.

“The offending comment and the reason for my apology to the police was my parting remark, ‘I thought you guys were supposed to f***ing help us.’ It was obviously wrong of me to use such bad language and I am very sorry about it and grateful to the police officer for accepting my apology.”

It is understood that Mr Mitchell, who was nicknamed “thrasher” at school, will make a statement to Parliament on his resignation next week.

He was previously International Development Secretary and one of the Government’s most steadfast backers of the policy to continue increasing public spending on overseas aid.

His promotion to chief whip appeared to seal his place at the heart of Mr Cameron’s team – despite Mr Mitchell’s position as campaign manager for David Davis in the last Conservative leadership contest. It is understood that the Chancellor recommended that Mr Mitchell be moved to the chief whip’s position in last month’s reshuffle.

However, the row over his confrontation with police had wider political significance as it led to accusations that senior Conservative politicians are out of touch with the general public and was seized upon by Ed Miliband to launch class-based attacks on the Prime Minister.

A friend of Mr Mitchell said on Friday night: “He is not blaming Labour – they were doing their job. He is not blaming anybody. A situation appears and it became impossible for him to continue in his job.”

Michael Fabricant, a former Conservative whip who has been openly critical of Mr Mitchell, said: “I spoke to Andrew yesterday about this and I was frank. This has been playing out like a long Greek tragedy and I hope that now he will take a break and rebuild his strength. He is a very able individual and I am sure he will return to public life in due course.”

The resignation was welcomed by representatives of the Police Federation, which represents rank-and-file officers, although there was some anger that he is refusing to accept the Downing Street officers’ version of events.

Stuart Hinton, secretary for Warwickshire Police federation who met Mr Mitchell last week to discuss the affair, said: “He has made the right decision. He has fallen on his sword and it is time to move on.”

Labour criticised the Prime Minister for looking “profoundly weak” by backing the chief whip for weeks.

Michael Dugher, a shadow Cabinet Office minister, said: “After weeks in complete denial, Andrew Mitchell has finally bowed to public pressure.

“David Cameron is left looking profoundly weak and totally out of touch, doing everything he could to hold on to Andrew Mitchell only for his Chief Whip to bow to the inevitable given the understandable public anger.”

Sir George Young, who quit as leader of the House in last month’s reshuffle, was appointed Government chief whip to replace Mr Mitchell.

Source: The Telegraph