Police in one county may be forced to stop attending vehicle crime and retail thefts worth less than £100, MPs have heard.
Bedfordshire police and crime commissioner Kathryn Holloway said there "could be an argument" that people should not be leaving valuables in vehicles.
Appearing before the Commons Home Affairs Committee, she suggested the force was having to look at what it is "not able to do" following budget squeezes.
She said: "Two examples that have been suggested are that we would not be attending vehicle crime.
"I suppose there could be an argument that people are insured and shouldn't be leaving valuables in cars, vans and so on.
"However, it's also been suggested that we wouldn't be going to retail thefts of £100 and under.
"I have no appetite whatsoever as the PCC for Bedfordshire in seeing my county become the retail theft capital for the UK."
Ms Holloway said Bedfordshire has a budget in the lowest quartile in terms of central government funding and local council precept.
She told the committee the force has made nearly £35 million in cuts and faces a further reduction of £11.4 million to £12.5 million in the next four years "if things remain unchanged".
Mr Khan added: "It's not conceivable that there is not going to be impact on the safety of Londoners."
The debate over police resources has been played out in public as ministers prepare to unveil the latest cash settlement for forces.
A string of senior figures have raised concerns over the capacity to meet challenges including an unprecedented terror threat and rising levels of violence without a funding boost.
The Association of Police and Crime Commissioners (APCC) has told the Home Office that £440 million extra is required in 2018/19 and £845 million in 2019/20.
But Home Secretary Amber Rudd has urged force leaders to focus on cutting crime instead of lobbying for more money.
Forces' approaches to some offence types have come under scrutiny in recent weeks.
Scotland Yard has suggested it is "not practical" for officers to spend considerable amounts of time investigating crimes such as shoplifting and criminal damage.
Last week, a watchdog warned that police are leaving "low priority" incidents and crimes unresolved for long periods, or without a response at all.
Figures show forces in England and Wales recorded increases across all theft categories in the year to June 2017.
The most marked were in vehicle theft crimes and shoplifting, which were up by 17% to 427,561 offences and by 11% to 377,172 offences respectively.
Statisticians say the recent rises should be seen in the context of a longer-term falling trend.