Scotland Yard detectives are expected to make swift arrests in a major criminal probe into the possibility that Jimmy Savile was at the centre of a network of child abusers who targeted more than 200 victims.

The vast majority of the victims allege they were abused by Savile. But detectives announced on Friday that they were mounting a full criminal investigation after some of the hundreds of people who have come forward in response to the unfolding scandal made allegations that they were abused by other individuals who are still alive. It is understood that most of these claims of sexual abuse relate to people who were associated with Savile in some way.

It is not known how many individuals are being investigated.

Commander Peter Spindler, from the Metropolitan police, said his officers were pursuing more than 400 lines of inquiry. They have uncovered allegations against living people that require a formal criminal investigation, he said.

The National Society for the Prevention of Cruelty to Children said it was now likely Savile was one of the most prolific sex offenders they have ever come across.

"We are dealing with alleged abuse on an unprecedented scale," said Spindler. "The profile of this operation has empowered a staggering number of victims to come forward to report the sexual exploitation which occurred during their childhood.

"I am pleased that victims feel confident enough to speak out about the abuse they suffered and would like to reassure the public that we take all these cases very seriously and they will be investigated with the utmost sensitivity."

The officer leading the criminal investigation, Detective Chief Superintendent Keith Niven, head of the child abuse investigation command, is running a criminal inquiry with no scene of crime and no forensic evidence. A source with knowledge of the investigation of child abuse reported by adults said officers would be looking for "chimes" in victims' accounts and corroborating details against suspects. The strength of a case against a suspect would be all the greater if a number of people have come forward with similar stories.

Experts in cases of child abuse reported by adults many years later say arrests are likely to take place quickly.

Jonathan West, a leading child protection campaigner who as a parent helped expose a 60-year-old sex abuse scandal at Ealing Abbey, in west London, said he was "not in the least surprised" that the Met police was now involved in a criminal investigation into other individuals.

"It is quite common that where one person is found to have committed child sex abuse in an institutional context – most likely a school but also in hospitals and now as we have discovered at the BBC – it is usually a sign that the institution's child protection practices are inadequate.

"And it quite often happens that more than one person manages to take advantage of that."

Peter Watt, the head of the NSPCC, said it had passed more than 136 calls directly relating to allegations against Savile to police. It now appeared, he said, that the late celebrity was "one of the most prolific sex offenders the NSPCC has ever come across."

"It's important we recognise the brave step victims have taken in coming forward and we urge any other victims to do the same," he said.

But Noreen Tehrani, a psychologist who works with adult victims of child abuse, warned that the impact on victims of such a high profile inquiry could be devastating and they would need specialist support.

"Forget that these victims are in their 40s and 50s now. What will happen is they will be thrown back to that traumatic event when they were a child," she said. "They will look back on what happened as adults and the guilt and blame will be greater. They will have to keep being told it was not their fault, they were a child. It's not enough for the NSPCC to provide a helpline number, these people will need specialist support. And I really worry about that, I really worry about these victims and who is going to pick them up as this plays out."

The Met police launched Operation Yewtree, its assessment of allegations involving Savile, a fortnight ago and has been flooded with information from members of the public, including alleged victims and witnesses.

On Friday, Greg Dyke, the former BBC director-general criticised the corporation's response to the Savile scandal.

He said the BBC should "have moved very quickly" to explain why a Newsnight report about allegations of sexual abuse by the late DJ was dropped.

"Someone had to explain why they took a decision not to do it because otherwise it left them looking suspicious and it looked like they had been leaned on because the BBC wanted to run two specials about Savile, which I don't believe would have happened," he said.

The Met has told the BBC that it can now begin its own internal reviews into alleged abuse by Savile.

Dame Janet Smith, who headed the Shipman inquiry, has been appointed to head an inquiry into Savile's time at the BBC, and Scotland Yard said it recognised "her need to progress this important work". Former head of Sky news Nick Pollard is carrying out a separate inquiry into why the Newsnight programme was pulled by the BBC.

It also emerged on Friday that the BBC was aiming to rush a special edition of Panorama into its schedules looking into issues surrounding Savile's years of abuse, which could be run on Monday.