Neumann called Prevent "right in principle" but said Britain had "over-securitised its anti-radicalisation policy" and thus risked alienating the people who could be its most effective partners.
In Paris, French President Emmanuel Macron said he had been informed of the new death toll.
He did not name the third victim.
Two men were arrested on suspicion of terrorism offences and a third man was arrested on suspicion of drug offences.
"We were happy that he was becoming more religious but did not know that in fact he was becoming a terrorist".
They tipped off the authorities in Britain and Morocco about him, but for reasons that are still unclear he was not on the radar of British police and intelligence services before Saturday's attack.
Both British authorities and Ireland's Police Commissioner Noirin O'Sullivan have said they had no evidence Redouane was involved in any terror cell during his time in both countries.
"I understand deep down, inside my heart, the pain of these people", she said, speaking at her home near the northern city of Bologna. Britain did not participate.
Authorities previously identified 27-year-old Khuram Shazad Butt and 30-year-old Rachid Redouane as the two other men who rammed a van into pedestrians on London Bridge on Saturday night, and then jumped out and began stabbing patrons in the crowded Borough Market.
The Metropolitan Police say the body was found Tuesday downstream from the bridge.
Mr Thomas's next of kin have been told, police said, but formal identification has not yet taken place.
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As outrage grows over the revelation that at least one of the London attackers was a well-known Islamist, authorities admitted Tuesday that their hands were often tied in tackling even known threats.
Seven were killed and almost 50 wounded.
"Detectives were appealing for information about Xavier Thomas, 45, a French national who had not been seen since the night of the terrorist attack on London Bridge".
Police said earlier that witness accounts suggested he might have been thrown into the river.
The hospital said Ms Boden was "an outstanding nurse and a hugely valued member of the staff team in Theatres Recovery, described by her colleagues as "one in a million" who always went the extra mile for the patients in her care".
Armed officers killed all three within eight minutes of receiving a 999 call.
So far four of those killed in the attack have been named.
No more than 20 seconds elapse from the officers leaving their ARV to the attackers lying still on the floor. Butt told the friend he had stopped attending al- Muhajiroun meetings some time ago.
He added: "On behalf of the United States, I want to offer heartfelt condolences and prayers and similar thoughts go out to the family of the man killed in Melbourne".
A 21-year-old Australian woman has been confirmed as one of the victims of the London terror attack.
"We are paying a heavy cost in these attacks", Macron said.
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