British police conducted more raids and detained more people in connection with the attack.
Britain's terror threat level will remain at "severe" after militants killed seven people and injured 48 in London, Prime Minister Theresa May said on Monday, describing the assault as an attack on the free world.
Three knife-wielding assailants rammed a van into pedestrians on London Bridge and stabbed others nearby Borough Market on Saturday night.
"JTAC, the independent joint terrorism analysis centre, has confirmed that the national threat level remains at severe. That means that a terrorist attack is highly likely," she told BBC television after a meeting of the government's emergency committee.
"It is now clear that, sadly, victims came from a number of nationalities. This was an attack on London and the United Kingdom, but it was also an attack on the free world," she added.
Britain has been on high alert since the recent attack on a concert by US pop star Ariana Grande in Manchester, north-west England, in which seven children were among the 22 dead.
British police investigating Saturday's attacks in London detained a "number of people" after entering two properties in early morning raids in the east of the city.
Police said officers from the Counter Terrorism Command unit had raided the properties and searches were ongoing in connection with the attacks.
"A number of people have been detained," police said in a statement after raids in east London, as commuters returned to the scene of the attacks after some security cordons were removed.
"A very high priority for us is to try to understand whether they were working with anybody else," London police chief Cressida Dick told BBC television.
Police seized "a huge amount of forensic material" after going through the van used in the attack "very very carefully," she said.
Police arrested 12 people in the Barking district of east London on Sunday following the attack, one was later released.
Saturday's night assault occurred five days before a parliamentary election and was the third to hit Britain in less than three months.
Dick said the attacks carried out by Daesh in Britain have been largely domestic plots and the majority of the threat facing the country is not directed from overseas.
"All the recent attacks I think have a primarily domestic centre of gravity," she said.
"We will always be looking to see if anything has been directed from overseas but I would say the majority of the threat that we are facing at the moment does not appear to be directed from overseas," she added.
Britain's government and local authorities are working closely with the police to guarantee security around Thursday's national election, and robust plans have been in place for weeks, May's spokeswoman said on Monday.
"There are plans in place for the general election. Police have been working closely with local authorities for several weeks on this. Those plans were developed with the threat level being at 'severe' so they are pretty robust," the spokeswoman told reporters.
"Police review security for all events but we have been working very closely with them and local authorities for some time."
National campaigning resumed on Monday after a one-day suspension out of respect for the victims of the London attack.
"Violence can never be allowed to disrupt the democratic process," May said outside her Downing Street office on Sunday.
Calls for resignation
Britain's opposition Labour leader Jeremy Corbyn has called on Conservative Party's May to resign after she presided over cuts to police budgets and numbers during her six years as interior minister.
Police numbers decreased every year during her time as interior minister from 2010 to 2016. In March 2016 there were 124,066 police officers in England and Wales compared to 1,443,734 in March 2010.
Asked if he would back calls made by others for May to resign, Corbyn told Sky News on Sunday that:
"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. Yes we do have a problem, we should never have cut the police numbers."
The former strategy adviser to David Cameron, Steve Hilton, also blamed May on Twitter over her security failures that led to terror attacks in Westminster, Manchester and London Bridge.
Hilton said May should be "resigning not seeking re-election."
Theresa May responsible for security failures of London Bridge, Manchester, Westminster Bridge. Should be resigning not seeking re-election pic.twitter.com/2o0odey2BQ— steve hilton (@SteveHiltonx) June 5, 2017