Authorities identified the three men believed to have launched the attack as Khuram Shazad Butt, Rachid Redouane and Youssef Zaghba.
Prosecutors in Italy say there was not enough evidence to arrest or charge the 22-year-old when he was intercepted at Bologna airport.
All three perpetrators were confronted and shot dead by armed officers within eight minutes of the first emergency call.
Seven people were killed and dozens wounded in the attacks by three assailants near London Bridge.
Amaq, an outlet affiliated with the Islamic State in Iraq and Syria (ISIS) group, said the attack was carried out by “a detachment of fighters from Islamic State”, referring to the group by its other name.
A man has been arrested on suspicion of terror offences by detectives investigating the London Bridge attack following an early morning raid at an address in east London.
Last year, Zaghba was stopped at the airport in Bologna on his way to Istanbul and was put on an EU-wide database but was not prosecuted.
A property in Ilford, east London, was also searched by police at about 01:30 BST, but no arrests had been made, the police said. Ireland’s national broadcaster RTE reported that Redouane had an Irish residency card and had lived in Dublin.
He was known to security services and even featured in a television documentary entitled “The Jihadis Next Door”.
The Italian reports said Zaghba was intercepted at Bologna airport a year ago as he was about to board a plane for Turkey, with the apparent intention of joining Islamic State militants fighting in Syria.
The Metropolitan Police specialist marine unit found the body last night.
At any one time there are about 500 active counter-terrorism investigations concerning 3000 people of interest. Another Australian who died, nurse Kirsty Boden, was said to have been trying to help other victims when she was killed.
Police are still appealing for witnesses as they piece together details of the attack. Her family described her in a statement as an “outgoing, kind and generous person”.
“It is a heavy toll that we pay in these attacks”, he added.
His girlfriend, who was hit by the vehicle, is seriously injured in hospital.
Thomas had been missing since he was caught up in the attack with Delcros. Citing local media, The Daily Telegraph said the national was 27 years old and he worked in the Boro Bistro in Borough Market.
“I managed to escape him, but my friend Alexandre did not have that chance”, he said.