Lincolnshire currently employs 1,189 officers.

“At what point does a police force lose its viability?” he asked. “We’ve got very good people who do good things with the resources they have at their disposal and I’m hugely supportive of that.

“But the bottom line is we can’t police on a shoestring.”

The county’s Conservative police and crime commissioner, Marc Jones, said officers had to travel long distances between towns to transport suspects because of a lack of custody suites and, with one of the biggest rural road networks, police units struggle to prevent high levels of traffic deaths and injuries.

Lincolnshire has around 60 neighbourhood officers covering 2,500 square miles. Grimsby, policed by neighbouring Humberside, has the same number of officers for a single town.

“It’s outrageous that our next-door neighbour can put as many neighbourhood police officers in one town as we can deploy across our whole county,” Mr Jones said, adding “that is not sustainable”.

Chief Constable Gibson said the funding issue was so stark, all of the county’s 60 neighbourhood officers could be at risk, which he argued would turn Lincolnshire into a purely “reactive” force.

He rejected the suggestion the force could find more savings. In recent years Lincolnshire has replaced police helicopters with drones, moved gun licensing online, and introduced mobile fingerprint units in an attempt to save money.

Rethinking the 2006 police funding formula could bring Lincolnshire an extra 10% to 12% more cash.

But better funded forces would lose money, creating a difficult political challenge for the government, so a new formula remains on the shelf.

A further funding announcement for future years is expected in April, and officials have indicated they might consider updating the funding formula.

The government is working on plans to improve the way police forces buy equipment and services, and to help forces share resources.

Officials say this will help forces balance budgets and improve services.