Campaigners have raised concerns about police recording systems after forces said it would cost too much to retrieve information on officers' criminal records.
The Press Association asked every force in the UK how many officers and police community support officers (PCSOs) had been convicted of offences since 2012.
Data was also requested on the number of serving staff with criminal convictions.
Nearly half of the 45 forces - 20 - declined to provide either part or all of the information asked for on the grounds that the work involved in complying would exceed cost and time limits.
The Freedom of Information (FoI) Act allows authorities to refuse requests if they calculate that the amount of work needed to retrieve the data means it will cost more than £450 to comply.
Guidance from the Information Commissioner's Office states that agencies should rate staff time at £25 per person per hour, regardless of whether the work is outsourced or done internally. This means a limit of 18 staff hours per request.
A handful of forces did not respond at all.
Katherine Gundersen, of the Campaign for Freedom of Information, said: "The variation in responses is striking.
"While it may be understandable that some forces aren't able to provide details of all convictions if this would require them to search through thousands of individual personnel files for historical convictions, it's a serious concern that many forces apparently have no efficient way of retrieving information about recent convictions.
"This raises questions about how effectively they monitor and record the criminal conduct of their own officers."
Figures that were provided revealed that 309 officers and PCSOs have been convicted of offences in the past three years, including sex crimes, assaults and possessing indecent images of children.
At least 295 police officers and PCSOs with convictions are currently serving, according to figures from 18 forces.
Most services refused to disclose the names of the officers involved in crimes, arguing that identifying them would breach data protection laws.
The Government has launched a review of the FoI Act to consider whether it should be harder for the public to obtain details about the inner workings of Whitehall.
Sir Jeremy Heywood, the head of the civil service, has suggested that fear of the FoI Act could lead to officials being "less candid" with Government ministers because their correspondence could be published.