Forces should get tough on "bad apples", say the Lib Dems.
More than 1,000 serving police officers in Britain have criminal convictions, the Liberal Democrats have reported.
More than half of the 1,063 convictions relate to speeding or other motoring offences; 77 officers have convictions for violence and 96 for dishonesty.
The Liberal Democrats, who obtained information from 41 forces, called the figures "staggering".
But the Police Federation denounced publication of the figures as a "petty attempt to discredit".
Paul McKeever, chairman of the federation which represents rank-and-file officers in England and Wales, said it was "baffling" that the Lib Dems "could be so keen to conduct this type of headline-grabbing expose.
"Not only do these figures serve to undermine confidence in policing by failing to appreciate the nature of these convictions but effectively ignore the thousands of successes achieved by the police each day," he went on.
"Are the Liberal Democrats effectively suggesting that a person caught and already punished for a minor offence should then be rejected from the police?"
The figures cover only those forces in England, Scotland and Wales which responded. The Police Service of Northern Ireland refused to answer the Lib Dems' request for information.
The most recent figures put the number of serving officers in the 51 territorial forces in England, Scotland and Wales at 159,359. This figure does not include the British Transport Police, Ministry of Defence Police and Civil Nuclear Constabulary - which were not covered by the Lib Dems' survey.
Serving officers who are convicted do not face automatic dismissal, but the Association of Chief Police Officers said it was "very rare" for people with convictions to be recruited by the police.
Each case was assessed on its merits, said Acpo.
"Where a minor offence is committed, it needs to be laid against the years of dedicated service by the officer to determine if it is more damaging to the community if an officer is not allowed to continue to serve," said Peter Fahy, Acpo's lead on workforce development.
"The force concerned will then take action depending on a range of factors including the severity of the offence and its impact on an officer's ability to carry out their duties," said Mr Fahy, who is Chief Constable of Greater Manchester.
The number of serving officers with convictions recorded in the data includes five who were sacked but then reinstated by the Home Office.
The figures also show that forces serving Durham, Surrey, Dorset, Greater Manchester, Lothian and Borders, and Grampian had a total of 132 serving officers with convictions, but none was dismissed.
Offences included a serious assault in Durham, four incidents of drug possession in Surrey and two incidents of misconduct in office in Manchester.
The total figure for Britain, which does not include cautions, is likely to be higher because some forces did not provide full details and 10 gave no information at all, said BBC home affairs correspondent Danny Shaw.
The figures showed 210 officers had been dismissed or required to resign in the past five years as a result of criminal convictions.
Of those with convictions for violent offences such as assault, battery and wounding, 77 had kept their jobs, and 45 had been dismissed in the last five years.
There are 96 serving police officers with convictions for offences of dishonesty, including theft, perverting the course of justice, fraud and forgery.
Chris Huhne: A few bad apples shouldn't be allowed to bring the force into disrepute
Liberal Democrat spokesman Chris Huhne said it was "worrying" that so many police officers with serious convictions had been allowed to keep their jobs.
"It is staggering that so many of the people entrusted to protect us from crime have criminal convictions themselves," he said.
"The public entrust the police with the use of legal force precisely because they are self-disciplined and restrained, which is why anyone convicted of a violent offence should be dismissed."
He added that those convicted of dishonesty could not perform their duties effectively, as they could not be relied upon as a witness.
"Police forces should get tough on bad apples," he added.
But Bobby Cummines, chief executive of Unlock, the National Association of Ex-offenders, said: "Hopefully this will encourage other public authorities, as well as private employers, to themselves respond more positively towards employees who obtain a conviction.
"Having a conviction should not be an automatic bar to any profession, and a case-by-case approach allows for an assessment of the individual circumstances. Otherwise, around one in five of the working population are automatically excluded."
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