Eight people were killed and dozens injured when three men launched a van and knife rampage on Saturday night.
Counter terror officers arrested a 30-year-old man in Ilford on the early hours of June 7, after a 27-year-old man was taken into custody in Barking, east London, on June 6.
"All three were arrested on suspicion of the commission, preparation or instigation of terrorism offences", the Met Police said in a statement.
The accused however are not connected to the 1 June attack in the United Kingdom capital that left eight people dead, the police said on Thursday.
Dramatic footage from London's Borough Market shows three attackers viciously stabbing a man just before police converge and shoot them all dead.
Xavier Thomas, 45, is thought to have been struck by the terrorists' van on the bridge and witnesses reported him being thrown into the water.
Ms Delcros is said to have been seriously injured.
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Scotland Yard said formal identification had not yet taken place, but Mr Thomas' next of kin had been informed.
London's Metropolitan Police confirmed on the Wednesday that the death toll from the London Bridge terrorist attack has risen to eight people.
The third suspect, 29, was apprehended at a home in the same area of the British capital.
Italian prosecutor Giuseppe Amato said there was not enough evidence to arrest or charge the 22-year-old when he was caught at Bologna airport last year.
The other two attackers were identified Monday as Khuram Shazad Butt and Rachid Redouane.
The attack, and prior attacks in Manchester and near Parliament in London, have prompted Prime Minister Theresa May to call for tougher counterterrorism laws even if it means changing human rights protections.
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