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The starting salary for police constables should also be cut, from the current £23,500 to £19,000 for someone with A-levels but no police-related experience or qualifications, Tom Winsor said.
And new educational requirements should also be brought in, with applicants needing three A-levels at A to C or equivalent qualifications, NVQ level three.
"It just makes a lot more sense," he said.
In the Metropolitan Police, more than half (52%) of its male officers are overweight, a fifth (22%) are obese, and one in 100 are "morbidly obese", the Winsor report showed.For women officers in the Met, a third (32%) are overweight, 16% are obese and 2% are morbidly obese.
Former West Midlands chief constable Sir Edward Crew, who worked on the review, said: "We are not looking for supermen."
Tom Winsor's report recommends officers should have to take an annual fitness test, with those who repeatedly fail, facing a pay cut.
An initial annual test requiring officers to reach level 5:4 on the bleep test should be brought in by September next year, Mr Winsor said.
This is equivalent to an average speed of 8.8kph (5.5mph) for three minutes 35 seconds, he said.
But this should get tougher by September 2018, along similar lines to the test currently used in Northern Ireland, which includes climbing over walls and pulling bodies.
Chief constables should be able to make any officer redundant as part of budget cuts, ending the prospect of a job for life, the review said.
Tom Winsor's review also recommends applicants should be able to enter the police service directly at inspector rank, and, "after rigorous testing", at superintendent rank.
Mr Winsor said: "It is clear that the existing pay system is unfair and inefficient.
"It was designed in 1920 and has remained largely unchanged since 1978."
But he added: "Officers who work on the front line, exercising their powers as constables in the most difficult circumstances, have nothing to fear from this review."
All police officers should be made to take an annual fitness test, with a pay cut for those who repeatedly fail, a review has said.
Tom Winsor, who has carried out the widest-ranging review of police pay and conditions in more than 30 years, said those who fail the test three times should be subject to disciplinary procedures and a pay cut.