Police are having to reclassify some crimes as "non-emergencies" because fewer officers are being made available to take 999 calls, police have said.
The Police Federation said officers were being taken off the front line to spend time "chasing statistics" to meet government targets.
A federation survey of 15 forces found the same problems recurring "time after time", vice-chairman Alan Gordon said.
He said burglaries and car thefts were often no longer seen as a priority.
Mr Gordon said government targets created by police reform meant forces had to form squads to deal with persistent offenders, rather than deal with emergencies.
He said: "These people are drawn from the front line, and the 24/7 response teams are left largely with probationers who are inexperienced and poorly supervised, and have to cater with an enormous workload.
"They are being run ragged."
'Chasing their tails'
Mr Gordon said some calls were being downgraded to allow police officers to deal with the high volume of work.
"Officers are turning up days after a burglary has been reported or cars stolen. These are calls that should get urgent attention to reassure the public."
Jan Berry, chairman of the federation, said targets had left police officers "running around in circles".
"The one element of policing that was always given priority was emergency response, and that now seems to be the one where we have got the least experienced cops, which arguably leaves you at the greatest risk.
"They are chasing their tails and it is hugely frustrating for those people."