Sources revealed the 23-year-old suspect had been referred to the Government’s anti-extremism Prevent programme several years ago amid fears he may have been harbouring extremist views.
Father-of-one Matt had spent almost 30 years in the force.
He is understood to be a former protection officer for Princess Diana.
Matt was shot in the chest at point blank range as many as five times after the suspect pulled a revolver from his trousers at Croydon custody suite as he was about to have a Covid check.
The suspect then turned the firearm on himself and was last night in a critical condition in hospital.
Investigators yesterday revealed the suspected drug dealer was in handcuffs at the time of the shooting.
The Independent Office for Police Conduct said Matt was shot just moments before officers would have found the gun during a weapons sweep with a metal detector.
Searched The suspect had earlier been arrested by a special constable and a regular officer on patrol after he was seen behaving strangely and suspected of being in possession of Class B drugs.
They searched him and allegedly found ammunition, before handcuffing him and driving him in a patrol car to the custody suite.
The man is understood to have been put into a holding cell. The sergeant then opened the door to get his personal details and go through the police station’s Covid-19 procedures.
Sources last night confirmed to the Daily Express the suspect is known to counter-terrorism police.
But they revealed the Prevent file was closed shortly after being opened.
Shocked colleagues battled to Friendly a fan in save the popular sergeant and he was rushed to St George’s Hospital in Tooting, where he later died.
Commissioner Dick said Matt was “big in stature, big in heart, friendly, capable, a lovely man and highly respected by his colleagues”.
He leaves girlfriend Sue and an adult son from a previous relationship.
Ms Dick said: “A lovely man, respected by his colleagues, officers, staff and of course by members of the public, including, I may say, suspects arrested or dealt with in custody.
“He was very well known locally and he will be remembered so fondly in Croydon and missed there, as well as in the Met and in the rugby world.”
He was due to retire in 2021, it was said.
A murder probe has been launched and investigators from the Independent Office for Police Conduct watchdog were on the scene to establish how the gun got into the custody suite.
Scotland Yard confirmed no police firearms were discharged in the incident.
Speaking from the scene, where floral tributes were left throughout the day, a friend who played rugby with the officer, described him as “an inspiration” who was looking forward to retirement.
The 27-year-old, who gave his name as Paul, said: “The man was a machine. He went from training with us last night to come to his shift work here in Croydon. He would do that week in and week out.”
New Zealander Matt came to the UK in 1989, joining Britain’s biggest police force two years later. He played rugby for London Irish RFC.
Previously based at Charing Cross Police Station, he was just 300m from an exploding IRA car bomb outside Downing Street in 1992.
It is understood he was also a protection officer for Princess Diana, the Queen Mother and former prime minister John Major. Matt had told a magazine in 1996: “I’ve got this photo of me as a kid wearing a police helmet. One of my uncles sent it over. I don’t remember growing up wanting to be a policeman, but now that I am I wouldn’t change it for anything.”
He is the 10th police officer to have been killed in the line of duty in the past decade – and the 17th killed by a firearm since the Second World War.
Home Secretary Priti Patel condemned the senseless killing as a “sad day for our country”.
Lissie Harper, whose husband Andrew was also killed in the line of duty, said: “Another hero has been taken from us in unwarranted violence. They protect us, but who protects them?” Borough commander Dave Stringer led a minute’s silence at 4pm outside the custody centre in Croydon where the officer was shot hours earlier at 2.15am.
Officers came outside the building and stood to attention in the car park and at the front of the building in tribute to their colleague.