Wayne Bowen, of Sheerness, Kent, fell from the roof of a revamped Peugot 309 on Tuesday night after kicking out a rear window and climbing on to the roof.
He was alone in the back of the 'escape-proof' car which had been stripped and fitted with a plastic interior and a perspex shield to separate prisoners from police officers in front.
A spokesman for Kent police said yesterday that a fleet of the new vehicles was introduced in the county six months ago. The spokesman said that manpower savings was considered one of the vehicle's attractive features.
At least two officers are needed in other vehicles; one to drive and the other to sit in the back of the car with the prisoner. The possibility of design faults in the vehicle will be part of the police investigation.
Mr Bowen was arrested during a disturbance at the Old House and Home pub in Sheerness on Tuesday night. He was wanted for questioning about criminal damage to a car earlier that day.
Mr Bowen was placed in the back of the converted police car. A woman police driver and male probationer were in front. The spokesman said Mr Bowen became violent, kicked out the car's rear window and climbed on to the roof.
Although the vehicle had no window-winding mechanism, internal door handles or locks, the redesign did not affect the standard glass windows.
As the driver tried to stop in icy conditions, Mr Bowen fell off the roof and under the car. Emergency services were called but Mr Bowen had already died.
The spokesman said: 'The man had been getting violent and was very agitated about being in the car. But unfortunately he got out and died in the process.'
The Police Complaints Authority has been informed and a full inquiry will be made. The officers in question have not been suspended.
'It was a really minor offence. We are baffled as to why he climbed out of the car.'
Mr Bowen was being driven seven miles to the nearest custody station at Sittingbourne by the PC and the probationer when he died.
Night cover was withdrawn from the Sheerness station last year to save manpower but Kent police say there is no direct connection between that and the introduction of the new cars.
Kent police said the adapted Peugeot 309 was not specially called to the scene to take the prisoner to the police station, it just happened to be the vehicle which responded to the call.
The Police Complaints Authority investigation will be conducted by Supt Ian Humphreys of Kent Constabulary. But members of Mr Bowen's family yesterday called for an immediate explanation.
'We just want to know why and how this could possible happen,' his brother-in-law, Tony Hewitt, said.
'There are lots of questions that need answers and we need those answers right now.
'The police have been very nice to us and sympathetic but they can't tell us what happened to Wayne and that's what we want to know.'
The new cars are thought be in use in Strathclyde, Wiltshire and South Wales. They are widely used in Europe.