Police chiefs have admitted that a second undercover unit stole the identities of dead children in the late 1990s or even more recently in a series of operations to infiltrate political activists.

Growing evidence of the scale of the unauthorised technique – nicknamed the "jackal run" after its fictional depiction in Frederick Forsyth's novel The Day of the Jackal – now means the number of families affected could total more than 100.

The Metropolitan police's deputy assistant commissioner Patricia Gallan told a parliamentary inquiry that both secret police units broke internal guidelines when they employed the technique, which MPs criticised as "gruesome" and "very distressing".

She had been called to give evidence to the Commons home affairs committee following the Guardian's disclosures that the Metropolitan police had secretly used the tactic without consulting or informing the children's parents in order to bolster their fake persona when operating undercover.

But, despite mounting concern over the practice, she declined to apologise to the families of the children until Scotland Yard had completed an internal investigation.

She said: "I do absolutely appreciate the concern and I understand the upset and why people are very distressed about this."

Keith Vaz, chairman of the committee, told her: "I'm disappointed that you've not used the opportunity to be able to send out a message to those parents who have children who may have had their identity being used that the Met is actually sorry that this has happened."

In another development, a family who believe that their son's identity was stolen as recently as 2003 has lodged a complaint against Scotland Yard. Barbara Shaw, the mother of a baby who died after two days, is pressing the police to reveal the truth and to issue an apology. She said she was deeply upset to discover that her child's identity was used in this way. "He is still my baby. I'll never forget him," Shaw said.

The Guardian has disclosed that, over three decades, undercover police officers in a covert unit known as the special demonstration squad had been hunting through birth and death records to find children who had died in infancy. Once they found a suitable candidate, they then created an alter ego to infiltrate political groups for up to 10 years. They were issued with official records such as national insurance numbers and driving licences to make their personas more credible, in case the campaigners in the groups they were spying on became suspicious and began to investigate them.

The SDS adopted the technique after it was founded in 1968. The evidence suggested that the unit stopped using it in the mid-1990s when officials records became more computerised.

However it now appears that the tactic has been used more recently by a second unit which started operating in 1999.

The National Public Order Intelligence Unit (NPOIU), which is still running, was also tasked with gathering intelligence on protesters.

Gallan told the committee that the practice "has been from the evidence I have seen confined to two units, the SDS and the NPOIU".

Pressed by MPs on whether the squads had gone "rogue" and had gone out of control, Gallan said they were operating at the time outside of police's guidelines for undercover operations. "From what I have seen, the practices at that time would not be following the national guidelines." She said the units had departed from the accepted practices, but she had yet to find out why.

MPs also heard allegations that a suspected undercover police officer stole the identity of the dead child, Rod Richardson, when he posed as an anticapitalist protester for three years.

Jules Carey, the lawyer for the family, told the committee : "I am instructed by one family who have a son who was born and died in 1973 and we believe that a police officer used the name Rod Richardson which is the name of the child and was deployed as an undercover police officer in about 2000 to 2003 using that name and infiltrated various political groups.

He added that the mother of the child "is upset about the circumstances in which the child died in 1973 and she is upset about the fact that the child's identity has been used as it has. She wants to know the truth about that. She would like an explanation as quickly as possible from the police".

The Met, in keeping with its standard policy, has refused to confirm or deny that Richardson was a police officer. However, when first informed about the case 10 days ago, they immediately launched an internal investigation.

Shaw said: "We believe we deserve an apology for what has happened. It's wrong that someone took Rod's identity like that without us ever knowing."

That complaint is one strand of a long-running investigation into the activities of the undercover officers stretching back 40 years. Gallan who was called to the committee as she is responsible for the inquiry, disclosed that 31 police staff are working on the investigation which was set up in 2011 and has so far cost £1.25m.

She also revealed that she had seen evidence since last September of one case in which a child's identity had been stolen by a police spy, but the child's parents had not been informed.

She did not give a commitment that the police would inform all parents whose children have had their identities stolen when their investigation ended, as there were "legal and ethical issues" to consider.

• This article was amended on Wednesday 6 February 2013. It said a senior officer had admitted that "a second undercover unit stole the identities of dead children as recently as the late 1990s".