The arrests in Barking, east London, followed a raid at a flat belonging to one of the three attackers.
A van hit pedestrians on London Bridge at 21:58 BST on Saturday. Three men then got out and stabbed people in nearby Borough Market.
The attackers were shot dead by eight officers who fired 50 bullets. A member of the public was accidentally shot.
Of the 12 people who were arrested, seven are women. A 55-year-old man was later released without charge.
Meanwhile, Canadian national Chrissy Archibald has been named by Canadian broadcaster CTV as the first victim of the attack.
A statement from her family said she “believed strongly that every person was to be valued and respected”.
It said she had worked in a homeless shelter until she moved to Europe to be with her fiance.
‘Range of injuries’
Assistant Commissioner Mark Rowley said the police had reacted knowing the attackers “had to be stopped immediately”.
“The situation these officers were confronted with was critical, a matter of life and death – three armed men wearing what appeared to be suicide belts,” he said.
The vests were later found to be hoaxes.
Mr Rowley said 36 people were in hospital with a “range of injuries” and 21 were in a critical condition.
Malik Ramadhan, a doctor at the Royal London Hospital, said his team had treated one man who had been shot in the head and was expected to make a full recovery.
Both London Bridge rail and Tube stations are due to reopen on Monday from 05:00 BST but the rail station will be exit only, Network Rail said.
The mother of 23-year-old Daniel O’Neill, who is recovering in hospital after being stabbed, told the BBC he had a seven-inch scar from the knife attack.
“He had just stepped outside the bar for a second and a man ran up to him and said ‘this is for my family, this is for Islam’ and stuck a knife in him,” Elisabeth O’Neill said.
“I’m still in shock. I can’t quite believe it’s happened.”
Sunday Express journalist and martial arts expert, Geoff Ho, who was injured, said that he helped defend a bouncer from the attackers outside the Southwark Tavern as it “isn’t happening on my watch”, his newspaper reported.
Meanwhile, “We believe we are experiencing a new trend in the threat we face as terrorism breeds terrorism,” Prime Minister Theresa May said in a televised statement on Sunday in front of her Downing Street office, where flags flew at half-mast.
“Perpetrators are inspired to attack not only on the basis of carefully constructed plots … and not even as lone attackers radicalised online, but by copying one another and often using the crudest of means of attack.”
She said the series of attacks represented a perversion of Islam and that Britain’s counter-terrorism strategy needed to be reviewed, adding: “It is time to say enough is enough.”