Police say they are uncovering a hidden “epidemic” of paedophile abuse in the 1970s and 1980s, with thousands of allegations leading to convictions against people who abused their power to attack children.

New figures seen by the Guardian show that 4,024 allegations led to guilty verdicts at court after police investigations since 2014 into decades-old child sex offences.

Officers say hundreds of offenders, including teachers, religious workers, youth and care workers, thought they had got away with their crimes. Many victims have been traumatised, and some have killed themselves or been left with severe mental health problems.

Police believe the figures, which show that 35% of all allegations led to guilty verdicts, demonstrate that inquiries into non-recent sexual abuse are not “spaffing money up the wall”, as Boris Johnson last year claimed. Labour said Johnson should apologise to victims.

Officers believe there are many more allegations to come, and Chief Constable Simon Bailey, the national lead for child protection and abuse investigations, told the Guardian: “We are now having to come to terms, as a society, and we are going to have to recognise and accept, that during the 1970s and 1980s in particular, there was widespread sexual abuse of children taking place.

“These allegations and the vast majority of cases were never reported to the authorities. Some victims did not think they were going to be believed. There was one constant factor: there was an abuse of power … to satisfy their sexual desires.”

Among those convicted were care home boss John Allen, 78, jailed for 14 years for attacking five child victims between 1976 and 1984, Timothy Mawer, 51, a badminton coach jailed for abusing seven victims in the 1980s and 90s, and John Clifford Davies, 61, a children’s home worker jailed for 24 years for a string offences in the 1970s and 80s.

The national operation coordinating claims of non-recent child sexual abuse began in 2014 and is called Operation Hydrant. It began after the Jimmy Savile scandal prompted more victims to come forward.

Since Hydrant’s launch, 7,000 suspects have been identified, with 11,346 allegations of attacks received from 9,343 victims, all concerning sexual abuse of children. Some claims date back to the 1940s.

Of the alleged offences, 47% were not investigated by police, in over a third of these cases because the suspect was dead. In a fifth of discontinued claims, suspects could not be identified. More than one-third of the allegations resulted in convictions at court, with 6% resulting in acquittal.

The conviction rate comes despite cases from long ago being harder to investigate because of fewer, if any, forensic clues.

Some paedophiles who had escaped justice were convicted of multiple attacks, with one found guilty of 78 offences, based on allegations made by 10 victims. It is the first time Operation Hydrant has released conviction figures for non-recent child sexual abuse. Bailey, who is chief constable of Norfolk police, said: “There was an epidemic of it in the 1970s and 1980s. We do not understand the true scale of it. There is a lot to come out. There are a lot more victims who are yet to come forward.

“The really difficult thing to come to terms with is the untold damage that’s been done to victims and survivors. Some could not cope. It’s the toll that it has taken on their lives. Some victims committed suicide. Some coped, some are in the mental care system. The horrors bestowed on these children are horrific.”

Contemporary cases of child sexual abuse are also rising. “Policing today is having to deal with the sins of the past,” the chief constable said, with some paedophiles who offended in the past still presenting a danger today.

Bailey said: “It is crucial we continue to listen to the voices of those abused and investigate allegations thoroughly and impartially, irrespective of when the offence took place.”

In March 2019, Johnson, while foreign secretary, tried to deflect criticism about police cuts and told LBC radio: “I think an awful lot of money, an awful lot of police time, now goes into these historic offences and all this malarkey, and you know £60m I saw has been spaffed up the wall on some investigation into historic child abuse? What on earth is that going to do to protect the public now?”

Reacting to the new figures, Louise Haigh, Labour’s policing spokesperson, said: “These were utterly sickening crimes, and, despite being shamefully undermined by the prime minister, the police have operated with integrity and the utmost professionalism in bringing perpetrators to justice in these cases.

“Those victims of child sexual abuse have seen a lifetime of torment now end in convictions. The prime minister should have the decency to look them in the eye and apologise for claiming it was a waste of money.”

Disastrous cases such as Operation Midland, where the Metropolitan police fell for the lies of a fantasist as they pursued bogus claims against high-profile figures, led to some scepticism about the need to pursue non-recent cases.

Police say “persons of public prominence” make up 3% of suspects and include 44 politicians, mostly at a local level, 60 people from the entertainment industry, 31 from music and 30 from the world of sport.

Allegations flooded in after the Guardian revealed claims of an abuse cover-up in football after Andy Woodward bravely came forward. A government inquiry into child sexual abuse and claims of a cover-up continues.

Gabrielle Shaw, of the National Association for People Abused in Childhood, said: “We know from what victims and survivors tell us that being able to report what happened to the police is healing for many people, sometimes even when a case cannot be pursued. Thirty-five percent of offenders brought to justice for non-recent abuse is very encouraging.”