Chief Constable Sara Thornton, head of the new National Police Chiefs' Council (NPCC), said that significant budget cuts and the changing nature of criminality meant that Britain's police force had to prioritise.
If someone had an iPad stolen from their home, "it could be" that an officer would not be dispatched to investigate, she told the BBC.
Thornton said that instead, officers were focusing on child sex offences, cyber crime and terrorism.
Thornton has said that forces need radical reform if they are to survive budget cuts.
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"Crime is changing in this country," she said.
"There are a lot less burglaries than there used to be, a lot less car crime, but the sorts of crimes that are on the increase - sexual offences, concerns about terrorism, cyber crime - that's where we really need to focus.
"We need to move from reacting to some of those traditional crimes to think about focusing on threat and harm and risk and protecting the public.
"Of course, we will still want to gather evidence, but we might do it in different ways."
She said police budgets had been cut "significantly" - by 25 per cent over four years - and they were expected to be cut further.
"Over 10 years we will have lost about 70,000 posts and I don't think it's possible to carry on doing what we've always done, as we will just fail the public but also cause unacceptable stress among our officers and staff," she said.