A public inquiry should be held into police undercover activities, an ex-director of public prosecutions says, as claims that officers used dead children's identities are investigated.
Lord Macdonald said an inquiry was needed to ensure such practices were no longer followed.
Two former Special Demonstration Squad members told the Guardian they used identity records issued in the children's names.
Scotland Yard is investigating.
The allegations mainly relate to the squad's operations in the 1980s. The practice has been known about for at least a decade.
They come a couple of years after an undercover officer was revealed as having infiltrated environmental protests groups where he had relationships with two women.
The Guardian newspaper reported that the squad stole the identities of about 80 children who had died at an early age.
The Met said the alleged practice was not something that was "currently" authorised.
According to the Guardian report, deceased children's identities were used by the undercover officers because they would stand up to scrutiny if birth records were checked.
The practice was carried out without consultation with the parents of the children, the report suggested.
Two former officers of the Special Demonstration Squad (SDS) are quoted as saying they were issued with identity records, like driving licences and national insurance documents, in the children's names.
A document seen by the newspaper reportedly indicated that such identities had been used by officers between 1968 and 1994.
The SDS was a unit whose officers were involved in infiltrating protest groups. It was disbanded in 2008, according to the Guardian.
A Met statement said: "A formal complaint has been received which is being investigated by the DPS (Directorate of Professional Standards) and we appreciate the concerns that have been raised."
It also announced an investigation into "past arrangements for undercover identities used by SDS (Special Demonstration Squad) officers".
Lord Macdonald it was "completely inappropriate" for officers to use a dead child's identity, or form sexual relationships with people they were gathering information on.
"How are you supposed to maintain a level of fair and objective evidence-gathering if you are having sex with the person you are targeting, fathering a baby and then abandoning it, using a dead child's identity?" he asked.
"These are all examples of areas in which the police have completely lost their moral compass and have completely failed to understand the boundaries.
"We don't know quite how these units were operating in days gone by. It looks as though they've effectively gone rogue. I am not at all clear how high up in Scotland Yard these sorts of operations were being organised."
He added: "What we really need is a public inquiry into undercover policing which takes evidence, takes advice, sets out some guidelines, sets out some mechanisms so we can be confident these sorts of procedures are not being followed today."
Chief Constable Alex Marshall, who took over responsibility for setting policy on undercover policing in England and Wales on Monday, said the use of dead children's identities was "very poor" practice.
"It sounds like the public interest has not been properly considered," he said.
However, he said he was not in favour of a public inquiry, as suggested by Lord Macdonald, as it would "take many years and cost a huge amount of money".
He said the newly launched college would set standards on undercover work.
Chairman of the Home Affairs Select Committee, Keith Vaz MP, said he hoped it would hear evidence about the tactics from a senior Scotland Yard officer on Tuesday.
Guardian journalists Paul Lewis and Rob Evans, who wrote the story, and some of the women who were duped by police are also due to appear.
Mr Vaz called the tactic of stealing identities "shocking, distressing" and "slightly inept", when identities could instead be manufactured.