Dozens of police officers could be put on trial for stealing the identities of dead children, and sleeping with female activists they were spying on, according to the police chief leading an inquiry into Metropolitan police undercover work against protest groups.

Mick Creedon, the chief constable of Derbyshire, also said his team would investigate claims from a police whistleblower, Peter Francis, that senior officers wanted him to spy on, and even undermine, the Stephen Lawrence campaign.

In an interview, Creedon offered a "100%" assurance the matter would be properly investigated. He said prosecutors were already being asked to consider whether criminal offences had been committed by generations of undercover operatives planted in protest groups over the past 45 years.

Earlier on Monday, David Cameron said he was "deeply concerned by revelations from Francis, a former undercover police officer who said he was asked to gather intelligence that could be used to "smear" the campaign for justice for Stephen Lawrence, who was stabbed to death in a racist attack in 1993.

The prospect that police officers could be prosecuted will alarm senior officers, who have struggled to manage the fallout from the revelations

On Monday morning, the prime minister's spokesman hinted that the government may order an independent inquiry into Francis's revelations. Any inquiry would have to "command the family's confidence as well as that of the public", he said.

Creedon is already investigating two top-secret Met units: the SDS, which was disbanded in 2008, and another squad – the National Public Order Intelligence Unit (NPOIU) – which still operates.

He said his review was particularly focused on the role of commanding officers: "It's looking right up the chain of command," he said. "We have mapped, putting it bluntly, every senior officer, every commander, every deputy citizen commissioner, right up to and including home secretaries."

The chief constable refused to be drawn on the specifics of Francis's allegations, but he said that, if proved, they would be "not something that would sit comfortably with any police officer".

Creedon was asked to take over the inquiry, Operation Herne, in February after it was revealed that operatives working for the two spy units had used the identities of dead children. Weeks later, he conceded that the use of dead children's identities had been "common practice" in the SDS, and had continued in the NPOIU until around 2001.

In the interview, parts of which are being broadcast on Channel 4 on Monday night, he told the Guardian and the Dispatches programme that he was getting advice on whether dozens of undercover police who used the identities had committed criminal acts. "That is a consideration. We are getting legal advice on that," he said.

"I am looking to operatives to explain why they did it and why they were trained to do it and how they did it."

Keith Vaz, the MP and chair of the home affairs select committee, has already called on Scotland Yard to inform parents whose children's identities were used.

But Creedon said it was highly unlikely he would contact the parents, because to do so would require confirming the false identities used by former operatives.

"The way the world is now, that will fizz around the internet networks instantly," he said, adding that he saw little benefit in "raking up" the issue with parents who would otherwise remain oblivious.

He also declined to apologise to women who had been duped into relationships with police spies. But he added: "This is completely abhorrent. I use that term carefully. It should not have happened and I've always been clear about that. Was it routine? Was it actually part of the tactics? Was it quite deliberate and was it a way of infiltrating, or was it an occasional consequence? I don't know the answer to that question right now."

Creedon said prosecutors would also decide whether operatives who had sexual relationships were breaking the law.

"Well, we need to get advice from the CPS [Crown Prosecution Service] about whether an undercover officer having a sexual relationship would be a criminal offence," he said. "We're waiting for that advice from the CPS, and it will be wrong for me to speculate."

Asked if the officers may end up in court, he replied: "It's a possibility, yes."

However, he said the use by police of deception in sexual relationships needed to be understood in a wider context. "Around the country there are many people involved in sexual relationships who lie about their status," he said. "There are many people who say they're not married when they are married. It happens."

Operation Herne, which is costing the Met £1.6m a year, was launched in 2011. A staff of around 30 officers – almost all of them Met employees – have been sifting through 55,000 documents and interviewing former undercover police officers and their supervisors. Four specific cases are being separately supervised by the Independent Police Complaints Commission.Creedon refused to be drawn on when the inquiry would be complete but Craig Mackey, the deputy commissioner of the Met, has previously indicated it may not conclude until 2016, meaning the five-year inquiry would have cost over £7.5m.

Creedon said he did not know if the findings of his inquiry would ever be made public.

He said he was determined to "keep some balance" in his investigation: "Herne is not about castigating the 100 or so SDS officers that served over 40 years, some of whom were incredibly brave."

The chief constable rejected the suggestion that it would be more appropriate for the inquiry to be conducted by an independent figure or regulator.

"There has always been public concern about police investigating the police, but I'll be brutally honest: there is no one as good at doing it as the police," he said. "We don't seek to hide things. We do actually seek to get the truth and we do it properly and I frankly find it almost insulting that people suggest that in some way, because I'm a police officer, I'm not going to search the truth."