Government chief whip Andrew Mitchell finally fell on his sword tonight after admitting that the row over his confrontation with Downing Street police made his position untenable.

After weeks of criticism, jibes and speculation over his future, Mr Mitchell said it was not fair to put his colleagues and family through such ''damaging'' stories any longer.

He insisted in a letter to the Prime Minister that he had not referred to an officer on the gate in Downing Street as either a ''pleb'' or a ''moron'' but acknowledged delivering, after being told he could not ride his bike through the main gates, the parting line: ''I thought you guys were supposed to f****** help us.''

Mr Mitchell has desperately clung to his position amid a mounting clamour over the past month for him to go. He did not attend last week's Conservative Party conference in Birmingham - neighbouring his Sutton Coldfield constituency - after admitting that his presence would be a distraction.

He sought - and failed - to win over Police Federation members by meeting them in his constituency and trying to explain his actions, last Friday. Labour leader Ed Miliband maintained the pressure when MPs returned to Westminster this week, calling him ''toast'' during Prime Minister's Questions.

Concerns were raised by backbench Tory MPs during a meeting of the party's 1922 Committee. Mr Mitchell's fate is believed to have been sealed on Wednesday when deputy chief whip John Randall reportedly had to be talked out of quitting in protest at his determination to cling on.

However, in his resignation later to Mr Cameron tonight, 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 both would wish. Nor is it fair to continue to put my family and colleagues through this upsetting and damaging publicity.''

Paul McKeever, chairman of the Police Federation of England and Wales, said Mr Mitchell's resignation ''seemed almost inevitable''.

Labour said Mr Mitchell should have gone earlier and questioned the Prime Minister's judgment in allowing him to remain place.

Shadow Cabinet Office minister Michael Dugher said: ''What people will want to know is why, when the entire country could see that what Andrew Mitchell did was wrong, the Prime Minister totally failed to act.

''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.''

Mr Cameron, who conducted his first major reshuffle only last month, must now appoint a new chief whip, potentially forcing further changes in the ministerial ranks.

Mr Mitchell thanked the Prime Minister for his ''tremendous support and loyalty''.

He added: ''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****** 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.''

Accepting his resignation, Mr Cameron said he was ''sorry'' to receive Mr Mitchell's letter but added: ''I understand why you have reached the conclusion that you have, and why you have decided to resign from the Government.

''I regret that this has become necessary, and am very grateful for all you have done, both in Government and in Opposition - as well as for the kind words in your letter.''

Andrew Mitchell's resignation letter to David Cameron in full:

"Dear David,

"It is with enormous regret - not least because of the tremendous support and loyalty you have shown me during recent weeks - that I am writing to resign as your Chief Whip.

"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 both would wish. Nor is it fair to continue to put my family and colleagues through this upsetting and damaging publicity.

"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.

"I am immensely grateful to you for giving me the opportunity to serve as your Development Secretary for seven and a half years, both in Opposition and in Government.

"I believe Britain, under your leadership, has made real progress in transforming the lives and the opportunities of some of the world's poorest people and that we will continue to do so as we deploy an expertise and commitment which show Britain at its best.

"I now intend to concentrate on serving my constituents in the Royal town of Sutton Coldfield to the best of my ability and giving you the strong support you rightly deserve from all members of the Conservative Party.

"With every good wish,
yours ever,
Andrew Mitchell."