Scotland Yard deployed undercover officers in political groups that sought to uncover corruption in the Metropolitan police and campaigned for justice for people who had died in custody, the Guardian can reveal.

At least three officers from the controversial Special Demonstration Squad (SDS) spied on London-based activist groups.

Mark Jenner, an undercover officer, used the identity "Mark Cassidy" in the 1990s to penetrate the Colin Roach Centre, which was named after a 21-year-old black British man who died in the foyer of Stoke Newington police station in north-east London. The campaigners worked with people who said they had been mistreated, wrongfully arrested or assaulted by police in the local borough – Hackney – which was at the time mired in a serious corruption scandal.

Jenner, who was married with children, had a five-year relationship with a woman he was spying on before his deployment ended in 2000.

A second SDS spy was used to gather intelligence on another group that represented the victims of police harassment and racist attacks in a neighbouring part of east London. The second spy, whose identity is not known, did not infiltrate the Newham Monitoring Project directly, but got inside associated groups and was able to monitor its activities.

The revelation comes a day after the Guardian revealed that Peter Francis, a former Met officer turned whistleblower, was asked to dig for "dirt" on the family of murdered black teenager Stephen Lawrence. The revelation provoked anger across the political spectrum, led by the prime minister.

David Cameron promised an investigation into what he called the "absolutely disgraceful" disclosure that police sought to discredit the Lawrence family in the weeks after their loved one was stabbed to death by a racist gang.

"To hear that, potentially, the police that were meant to be helping them were actually undermining them – that's horrific," Cameron said.

Boris Johnson, as mayor of London ultimately responsible for the Met, describing the Stephen Lawrence revelations as "deeply, deeply unsettling".

In an urgent Commons statement Theresa May, the home secretary, told MPs she would ask two ongoing inquiries to investigate the Lawrence revelations.

But Neville Lawrence, Stephen's father condemned the response as "completely unsatisfactory".

He said: "I am convinced that nothing short of a judge-led inquiry will suffice and I have no confidence that the measures announced today will get to the bottom of this matter."

Francis said the Met planted a number of spies in groups that politically opposed the force. Of the Newham Monitoring Project, Francis said: "Every single event they were organising was being reported back to the SDS. We knew everything that was going on in the NMP."

Francis, using the alias of Pete Black amongst others, went undercover in a group called Youth Against Racism in Europe between 1993 and 1997. He said he was specifically asked by his superiors to gather intelligence on the so-called "black justice campaigns", which were seeking justice for mostly black or Asian men who died either in custody or after contact with police. Many of the campaigns were led by grieving relatives – although more radical groups also campaigned alongside them.

Francis recalled one episode during which he attending a candlelit vigil outside Kennington police station, for a man who had died after police contact. "I found myself questioning the morality of my actions for the first time," he said.

"To some extent these campaigns had been taken over by extremists but at their heart were families who had lost their loved ones and simply wanted justice. By targeting the groups, I was convinced that I was robbing them of the chance to ever find justice."

On Monday night, after being asked to comment on the latest disclosures about the deployment of undercover officers in police monitoring and black justice groups, Scotland Yard replied with a general statement from the commissioner, Bernard Hogan-Howe, on the Lawrence revelations. Hogan-Howe said that he was "personally shocked by the allegations that an undercover officer was told to find evidence that might smear the Lawrence family". He added: "It's imperative that we find out the truth about what happened as quickly as possible."

The full details of Francis's deployment are charted in Undercover: The True Story of Britain's Secret Police, which will be published on Tuesday.

After telling MPs they should show "zero tolerance of police corruption and wrongdoing", the home secretary said the latest revelations would be handled by an existing inquiry into allegations of corruption in the murder investigation into Lawrence's death which is being conducted by a barrister.

May said the issues raised by Francis would also be dealt with by an internal Met police review which has been ongoing since 2011. Operation Herne – which the Met has indicated will not conclude until 2016 – is being overseen by the chief constable of Derbyshire Police.

Herne is also investigating why undercover police adopted the identities of dead children and developed long-term sexual relationships with the people they were spying on.