One of the three attackers who killed seven people near London Bridge on Saturday night was previously investigated by British security services but had not been viewed as a serious threat, British police said on Monday.
Khuram Shazad Butt, aged 27, was a British citizen born in Pakistan, who was already known to police and Britain's domestic spy agency MI5, London's police force said.
"However, there was no intelligence to suggest that this attack was being planned and the investigation had been prioritized accordingly," police said in a statement.
The second attacker was named as 30-year-old Rachid Redouane, who police said claimed to be Moroccan and Libyan, and also went by the name Rachid Elkhdar with a different date of birth. Both men lived in the same area of east London.
Police said they were still working to establish the identity of the third attacker. Late on Saturday the three attackers drove south across London Bridge, mowing down pedestrians before stabbing bystanders in the nearby Borough Market area.
British police are stretched by the number of people they believe could potentially commit an act of terrorism. There are 500 current investigations involving 3,000 potential suspects.
"A small number of the highest priority investigations involve current attack planning, and these investigations command a significant proportion of our resource," police said.
Prime Minister Theresa May came under pressure from the media and the opposition Labour Party on Monday over cuts to police funding during the years when she was interior minister.
Saturday's attacks - which in addition to the seven dead left dozens in need of hospital treatment, including 18 in a critical condition - came less than a week before Britons vote in a national election.
"Our work necessarily involves making difficult judgments about how to prioritize the resources available to us at a time when the UK is facing a severe and high tempo terrorist threat," police said.
(Reporting by Andy Bruce, writing by David Milliken; editing by Guy Faulconbridge and Kylie MacLellan)