* Senior UK minister admitted swearing at police
* Row fuelled view Cameron's government is elitist
* Opposition say prime minister weakened by affair
By Tim Castle and Michael Holden
LONDON, Oct 19 (Reuters) - British minister Andrew Mitchell resigned on Friday after failing to shake off accusations he called police "plebs", an insult laden with snobbery that fuelled perceptions Prime Minister David Cameron's government is out of touch with voters.
Mitchell, the "Chief Whip" responsible for keeping discipline among lawmakers in Cameron's Conservative Party, denied using the offending word but admitted swearing at officers after being told to get off his bicycle as he left Downing Street last month.
"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," he said in a resignation letter to Cameron.
Cameron, educated at the elite Eton private school, has struggled to shake off the impression that he and other senior members of his party come from a rich, privileged background far removed from the electorate, and the accusations against former investment banker Mitchell have proved highly damaging.
With the Conservative Party behind in opinion polls, and an ailing economy struggling to recover from recession, the storm around Mitchell reinforced an image of a government divorced from Britons hit by budget-crunching austerity measures.
Mitchell's confrontation at security gates outside Cameron's office came just days after two unarmed female police officers were shot dead in the northern city of Manchester, adding to public disquiet at his reported behaviour.
Police representatives, already upset with the government over cuts to force budgets and changes to their working conditions, had demanded Mitchell quit, saying his disagreement over what had been said was an insult to all officers.
George Young, a veteran Conservative lawmaker who also attended Eton, was named as the new chief whip.
Mitchell's resignation had been inevitable, said Paul McKeever, chairman of the Police Federation of England and Wales, which represents frontline officers.
Cameron had hoped to retain Mitchell who he had only just moved to the chief whip job in a wide reshuffle of cabinet posts in September, but had been forced to repeatedly defend him.
"I regret that this has become necessary," Cameron said in a letter replying to Mitchell. "I wanted you to bring your organisational skill and energy to the important job of chief whip."
In recent months, the government has been beset by a number of high-profile mis-steps and policy U-turns after an unpopular budget. Just this week, Cameron sowed confusion among his own government by announcing a surprise pledge to curb energy prices for consumers.
Cameron's handling of the Mitchell affair has given more ammunition to critics who say his leadership has gone awry, with the opposition Labour Party saying it had left him looking "profoundly weak".
"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," said Labour lawmaker Michael Dugher.
Although Mitchell had apologised for his outburst, the political row had refused to die down because he refused to reveal what he actually had said.
"It was probably a misjudgement on Cameron's part not to encourage him to go straight away. He should probably have seen this wasn't going to be the kind of thing that could be lived down," said politics professor Tim Bale from London's Queen Mary University.
While reports that Mitchell called the officers "morons" were embarrassing, more damaging was the report that he used the word "pleb", a term that is soaked in upper-class condescension.
Mitchell addressed the issue in his resignation letter, giving Cameron his "categorical assurance" that he had not used the offending words. "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," Mitchell wrote.
"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'."
Mitchell, a former U.N. peacekeeper, was previously minister for international development. Cameron had made him chief whip in the hope of keeping greater check on rebellious Conservative legislators who want Britain to renegotiate its relationship with the European Union and recently forced a policy U-turn over reform of parliament.
However, his job of keeping other legislators in line had looked increasingly untenable when his own credibility continued to be undermined.