The British Transport Police said one of their officers, among the first to arrive, took the attackers on armed only with his baton and was seriously wounded.
The second alleged attacker was identified by police as Rachid Redouane, who alternately used the surname Elkhdar, and claimed to be Moroccan and Libyan.
Officials will also face scrutiny for failing to act on at least two reports about Butt's behaviour, one to the police from a neighbour who feared Butt was trying to radicalise children, and another to anti-terror hotline claiming he had been watching clips of a hate preacher.
Deadly attacks by Islamist militants in Paris, Nice, Brussels, Berlin, Manchester and London over recent years have shocked Europeans already anxious over security challenges from mass immigration and pockets of domestic Islamist radicalism. The pair were on London Bridge when she was struck by a speeding van driven by terrorists which continued to the other end of the bridge before the three men jumped out and began attacking people with knives. Britain's most senior police officer Cressida Dick said police resourcing needed to be revised.
An armed police officer stands on Borough High Street as police respond to Saturday night's terror attack on London Bridge.
It is not clear how having more police on the beat would have prevented the attack, since the men were shot dead within eight minutes, but the issue of police cuts has come back to haunt May, who served for six years at home secretary under her predecessor David Cameron before she became prime minister last year.
A spokesperson for Khan Sunday called Trump's remark "ill-informed" and said it took the mayor's words out of context.
May did not answer repeated questions on the cutbacks but said counter-terrorism budgets had been protected and police had the powers they needed.
That had been undermined by the last two attacks, he said: the Manchester attacker, Salman Abedi, must have had someone teach him how to make the bomb, and the London attack involved three people.
It followed President Trump deriding and misrepresenting Khan's attempt to calm Londoners after the attack.
The political tempo picked up again Monday with May saying opposition Labour Party leader Jeremy Corbyn is unfit to handle security and Brexit.
A similar attack took place on March 22, when a man drove his auto into pedestrians on Westminster Bridge in London, killing five people including the attacker himself, and injuring at least 50 more. Detectives are still working to identify the third attacker.
On Sunday, more than 24 hours after the attack occurred, the Islamic State terror group claimed responsibility for the attack. He led the three who ploughed into pedestrians before stabbing people in pubs, bars and restaurants.
The 30-year-old Canadian from British Columbia was in London for the weekend with her fiance, Mr Tyler Ferguson.
48 people have been injured, with 21 of them in a critical condition, according to the London ambulance service.
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