But in two-thirds of forces clear-up rates for burglary have fallen.
The Police Federation has described the performance indicators as 'misleading'.
Federation chairman Fred Broughton said there was a danger chief officers would be tempted to concentrate on the few tasks measured by the indicators to achieve a place at the top of the league table.
'There is a lot more to British policing than just measuring how long it takes to get to a call or measuring how efficient policing is in terms for clear-up rates for crime'.
The Audit Commission also reports that fire brigades are among the most consistently efficient services provided by local government. It says on average they met nationally set target times for responding to calls 95% of the time.
Audit Commission comptroller Andrew Foster said the report was generally a good news story for the public and the police. The police had improved their performance in clearing up violent crime, which was what the public was concerned about.
This was the first time the commission had included a measure of how much time the police spent in public. Uniformed officers on average spend less than half their time pounding the pavements.
Mr Foster said he believed police authorities and chief constables would be looking at this to see how they could improve police visibility on the streets, which was something the public wanted.
Sussex Chief Constable Paul Whitehouse commented: 'Monitoring what we do is essential. Where we have to be careful is how we use the data, and there are two points here.
'First of all, as the Audit Commission point out in their document, they only measure a very small proportion of our work and we provide an enormous other range of services which is not counted in here, and the public welcome those services. We need to work with the Audit Commission on ways of measuring them too so we don't skew our activities and do only the things that are measured.
'Secondly, we need also to remember that some of the things that we do can be very successful and yet they militate against other measures. For example, if we are catching more burglars by having more police officers operating in plain clothes proactively then we will have fewer officers available in uniform to reassure the public'.