Police could be disciplined if they fail fitness tests
Police officers' fitness could be checked annually with disciplinary procedures facing any officer who fails the test three times.
The recommendation is among major changes to police pay and recruitment in an independent review commissioned by Home Secretary Theresa May.
The review, by Tom Winsor, says there should be higher minimum educational standards for new police recruits.
It says some should join directly as inspectors and superintendents.
The BBC's home affairs correspondent Danny Shaw said under the review - which only affects England and Wales - chief constables would have powers to make police officers compulsorily redundant to cut costs - at present they can do this only if police have served for 30 years or more.
There would also be new powers to remove police officers who are on restricted duties and cannot return to work.
The report found 52% of male officers in the Metropolitan Police were overweight, 22% obese and 1% "morbidly obese".
But the former West Midlands chief constable Sir Edward Crew, who worked on the review, said: "We are not looking for supermen."
In a response to the report, the Police Federation's Chairman, Paul McKeever, said: "Police officers have had enough of the constant state of uncertainty and the deliberate, sustained attack on them by this government.
"They want to get on with the job they joined to do, serving their communities, and they expect the support of government. Instead they find themselves contending with cuts to pay and conditions of service, increased stress and pressures."
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."
Mr Winsor suggests police constables' starting salaries should be cut by up to £4,500, pointing out that vacancies are often "heavily oversubscribed".
Starting salaries would fall from £23,500 at present to £19,000 or £21,000, depending on qualifications.
Constables would be able to move up the pay ladder more quickly but a "specialist skills threshold" should be introduced at the final pay point of all officer pay scales.
This would consist of a "rigorous test" of the knowledge and skills required in each role and rank.
The retirement age would be raised to 60 and a new system of negotiating pay rates set up.
Home affairs select committee chairman Keith Vaz said he would call Mr Winsor to appear before the committee to "explain his intentions in more depth".
"We need to ensure that we will not create a two-tier system where performance is measured on the number of arrests rather than on benefit to the public," Mr Vaz said.
He called on the government to pause and discuss the "potential damaging impact" of the recommendations with the police and the public.
Mr Winsor says, together with the reforms already being implemented under the first part of his review, there would be gross savings of £1.9bn over six years, two-thirds of which will be re-invested in policing.
Mr McKeever said police officers had already made a significant contribution to tackle the national debt: "We've seen a minimum 20% cut to the police budget; the loss of 16,000 police officers expected over the next 4 years; £300m removed from police pay; increased pension contributions; a two-year public sector pay freeze and then a capped 1% increase in years three and four.
"How much more are police officers expected to take?," he added.
The Association of Chief Police Officers' lead on workforce development, Chief Constable Peter Fahy, said: "Police forces are facing a huge financial challenge but the need to reform the way our staff are rewarded and developed is not driven by money alone.
"Policing has become far more complex and specialised. Our staff want to see their individual talent and contribution recognised and the public want to see police effort targeted where it will have most impact.
"Chief officers have been clear that we will need radical approaches to absorb the current and future budget cuts and maintain the protection of the public. At the same time we must not put in danger the core ethos of service and self-sacrifice in policing that has served this country well."
Bernard Hogan-Howe, commissioner of the Met Police, the UK's largest force, said he supported the "broad thrust" of the review but suggested the numbers of those allowed to join at inspector and superintendent level should be limited in the first few years of the changes.
On the fitness test proposals, he said: "It is right and proper that police officers should do everything they can to keep themselves physically fit. If they are failing in that responsibility, it is only right that they should face some kind of sanction.
"But it is important that we put in place safeguards to protect those officers who have been injured on duty whilst fighting crime."