Police funding cuts could see forces stop investigating offences like petrol theft and vehicle crimes, MPs were told.
The Home Affairs Select Committee heard that decisions would have to be made about what crimes would have to be prioritised.
Pursuing people who make off without paying for petrol was given as one example of the type of offence Surrey Police would no longer be able to investigate, its Chief Constable Lynne Owens said.
But committee chairman Keith Vaz asked her: "Is this a green light to the criminals that you can come to Surrey, fill up your car with petrol and make off and you will not be pursued?"
She replied: "If we have a repeat vehicle, or a repeat person, or repeat location there is always going to be a requirement on policing to respond.
"We are not a civil debt recovery agency and there are too many examples where policing has moved into gaps caused by others, and it is those gaps that need to be filled," Ms Owens added.
Seven of the UK's most senior police figures have threatened the Government with legal action over the "potentially serious implications" of further police funding cuts.
Six police and crime commissioners have been joined by Stephen Greenhalgh, London's deputy mayor for policing and crime, in urging the Government to delay a decision on force budgets expected in this month's spending review.
In a letter to policing minister Mike Penning, the group said changes to the police funding formula would result in cuts that are "unfair, unjustified and deeply flawed".
Arguing that the Government had ignored its own consultation guidelines in drawing up reforms to the police funding formula, it said: "Regrettably, we feel the most recent consultation to be wholly inadequate.
"We have been given just three weeks to consider and comment on major revisions to the initial proposals. This is not in keeping with the Government's own guidelines on consultation, which were also ignored for the original consultation."
The letter highlighted the effects police cuts could have on its signatories' forces.
Speaking at the committee, Ms Owens also highlighted that funding cuts could mean officers would no longer be able to visit some victims of vehicle crime.
"Whereas previously we might have gone and visited a victim of vehicle crime we might not visit a victim of vehicle crime in the future," she said.
Labour committee member Chuka Ummuna, asked Ms Owens, Leicestershire Police Chief Constable Simon Cole and Lancashire Police Chief Constable Steve Finnigan, if they would be able to continue to protect the public.
Mr Finnigan replied: "It makes our mission or purpose - which is essentially to keep people safe from harm, and especially the most vulnerable in our communities - absolutely very difficult.
"And I think there is no doubt, at those levels of cuts, people in Lancashire will not be as safe as they are now."
He added that morale in his force was "pretty low", and that the situation was "unprecedented".
Mr Cole replied that the impact of the cuts on his force would mean it would have to deal with things differently, and that it would no longer be able to deal with as many things by "presence".
"It will mean that we will have to have a high tolerance of risk," he said.
Chancellor George Osborne has asked ministers in non-protected departments - such as the Home Office - to come up with reductions in their budgets of between 25% and 40% by 2019/20 ahead of the Comprehensive Spending Review (CSR) on November 25, when the Government's plans for the next four years will be set out.
Metropolitan Police commissioner Sir Bernard Hogan-Howe has previously said he is worried for the safety of London if the Chancellor announces cuts of £800 million or more over the next four years, while Mr Finnigan warned that expected budget reductions of £60 million will mean his force will "not be viable as we see it today" by 2020.