The Government-commissioned review of pay and conditions states that as many as three-quarters of policemen in some areas are overweight and obese, and that the public would be "surprised" to learn that their physical condition is never assessed during their careers.
It warns that unfit police officers could put themselves, colleagues and the public in danger if they are unable to tackle criminals, and points out that during last summer's riots they had to confront mobs while wearing heavy protective equipment.
The comprehensive study by Tom Winsor, the former rail regulator, recommends that in 2013 all police officers, including senior ranks and chief constables, should have to take annual fitness tests.
At first these would just comprise the "shuttle run" currently included in recruitment assessments, running to and fro on a 16yd track. The report notes than men in their sixties and of average fitness can "easily achieve" the required level, known as 5:4, which is equivalent to running at 5.5mph for 3mins 35secs.
But by 2018 Mr Winsor wants a more "stringent" assault course-type test introduced, similar to the one used in Northern Ireland that involves crawling, jumping, balancing on a beam, climbing over a wall and dragging a body.
Anyone who fails the annual test three times would face "unsatisfactory performance or disciplinary procedures", which could lead to a pay cut.
The report's authors insisted they were "not looking for supermen", merely ensuring that officers were able to carry out their jobs properly.
"Running after a suspect, or apprehending a violent or disturbed person, requires physical fitness and strength. A non-specialist officer who cannot do these things is incapable of some of the most elementary parts of police work, and when deployed may be a danger to himself, his colleagues and the public."
It went on: "During August 2011, there were cases of senior officers leading their officers in confronting and tackling violent and dangerous rioters. It is also appropriate that senior officers should set an example of physical capacity, resilience and fortitude in their leadership of their officers and staff, as they do in other respects."
It is claimed that fitter officers will be better at their jobs and sickness absence may fall as a result, although if many officers fail the running tests they may end up on "restricted duties" that could lead to their retirement on ill-health grounds.
The study warns forces that officers who would likely fail the test because of a medical condition, rather than an "unhealthy lifestyle", should not be discriminated against but rather given a more appropriate job.
It claims that in the 19th century, policemen often walked 20 miles a day on the beat, and worked seven days a week in shifts lasting up to 12 hours.
But in recent years officers have increasingly used cars and motorbikes to get around while specialist teams often work in offices rather than patrolling the streets, while the general population has also become more sedentary.
As a result, tests taken by the Metropolitan Police in 2011 found that just 25 per cent of male officers and staff were of normal weight, with 52 per cent overweight, 22 per cent obese and 1 per cent morbidly obese. Of the women surveyed, 50 per cent were of normal weight with 32 per cent overweight, 16 per cent obese and 2 per cent morbidly obese.
These rates of obesity are higher than those recorded in the general population.