The three, who include Paul Condon, the Metropolitan Police Commissioner, describe so-called 'noble cause corruption', that is, breaking the rules to ensure convictions.
At its most extreme, this involved planting and embroidering of evidence, faking notes and threatening beatings, they say.
Mr Condon, who recently spoke about the importance of tackling racism in the force, told BBC 1's Panorama programme that 'quite often the truth was the casualty' in the process of convicting criminals.
'I think there was a time when a minority of officers were prepared to bend the rules. I think they were prepared to massage the evidence - not for personal gain or not even, in their own terms, to tell lies about people. But I think elaborating on things that were said in a way to make sure that the case had the strongest chance of going through to a conviction,' he said.
'That was wrong. I don't justify it but I think can explain it in its historical context.'
Charles Pollard, Chief Constable of Thames Valley Police, said: 'There was a lot of scope to manipulate the system to ensure that you got confessions. No doubt about that. The system made it like that.
'Everyone knew it happened like that, judges, magistrates, the whole criminal justice system had a sort of conspiracy that is the only way you can make the system work. If you didn't do it that way, you couldn't actually convict guilty people and that needed to be done.'
He added: 'We have seen detection rates falling significantly. Part of that has come from a lot more crime being committed.
'But it also comes from this change from going for convictions through confessions to convictions through a whole range of other measures which are ultimately less effective . . . but more honest.'
Keith Hellawell, the Chief Constable of West Yorkshire, said people were 'physically frightened' of being in a CID office, 'whether those consequences were real or perceived. And of course many detectives would use that perception of violence rather than the violence itself.'
He added: 'Certainly, I've never used violence. The perception of violence, I suppose to be fair, yes.'
Asked how he would do that, he said: 'I was a very big officer, I was over 18 stone in weight. All detectives in those days were big guys.
'I would take my coat off, the criminal would perceive that that act was going to be followed up by a thumping or a fist or something, and therefore that put that person ill at ease and certainly more likely to tell me what they wished to tell me.'
The programme, 'Fair Cops', asks whether a new generation of senior officers can clean up the police without taking a soft line on crime.Reuse content