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More than 40,000 reported crimes including violent offences were not recorded by three forces, figures show.

As a result Kent and Cheshire have been rated inadequate and Cambridgeshire requires improvement, HM Inspectorate of Constabulary (HMIC) said.

Cheshire and Cambridgeshire improved but had more to do, while Kent's performance "slipped significantly".

Cambridgeshire and Cheshire said they were making progress. Kent said it accepted the findings.

The three are the latest to be inspected as part of a programme across forces in England and Wales.

Insp Zoe Billingham, of HMIC, said the Kent force had "taken its eye off the ball as a result of poor supervision" and audit inconsistencies had led to "false-positive" results.

"The force thought it was still doing the right thing whereas in reality its crime recording standards were slipping," she said.

Cheshire had improved but needed to do more Insp Mike Cunningham, of the inspectorate, said.

He said the force failed to record more than 11,600 crimes, but added: "We found that some serious crimes such as violence and sexual offences were being actively investigated but had not been recorded as a crime."

Source: HMIC

Insp Billingham said Cambridgeshire had implemented previous recommendations.

But she said: "It was accurately recording about 88% of all crime reported to it - which means that more than one in 10 crimes were not making it on to the books."

Cambridgeshire's Assistant Chief Constable Dan Vajzovic said the force had improved.

"While it is of concern that some crimes are being recorded differently and this needs to be addressed, my focus remains firmly on protecting and safeguarding our communities," he said.

Cheshire's Deputy Chief Constable Janette McCormick, said: "While we agree that there have been some crime recording errors, this does not mean we are failing victims, nor does the report call into question the integrity of officers and staff."

Kent's Chief Constable Alan Pughsley said all crimes not recorded had been reviewed.

He said the force was working to increase its accuracy, with extensive training under way.

"We have worked hard with HMIC to improve our crime data integrity, not just for the last year, but going forward, and will not rest until we are satisfied it is the best it can be," he said.