One of the three attackers who killed seven people near London Bridge was previously investigated by British security services but had not been viewed as a serious threat, British police said.

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 prioritised 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. Sky News reported on Monday that police had also found Molotov cocktails in the back of the attackers' van.

British police are stretched by the number of people they believe could potentially commit an act of terrorism. There are 500 current investigations involving 3000 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.

Asked if he would back calls made by others for May to resign, Labour leader Jeremy Corbyn told Sky News: "Indeed I would. Because there have been calls made by a lot of very responsible people on this, who are very worried that she was at the Home Office for all this time, presided over these cuts in police numbers and now is saying that we have a problem.

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 judgements about how to prioritise the resources available to us at a time when the UK is facing a severe and high tempo terrorist threat," police said.

Seven women and five men were arrested following the attack, while a 55-year-old man and 53-year-old woman arrested at the same address in Barking have been released.

Six women aged between 19 and 60 and four men between 27 and 55 are still being held by police.

Police raided properties in Barking on Sunday and two on Monday in nearby Newham and Barking.

On Monday evening, a crowd of all ages and races stood quietly for an impeccably observed minute's silence at a vigil a short walk away from the scene of Saturday's bloodshed.

London mayor Sadiq Khan warned extremists they will never win as mourners gathered at the service in Potters Fields Park, near London's City Hall.