With a general election set for Thursday, the main political parties suspended campaigning on Sunday as a sign of respect for the seven people killed and the scores wounded when three men drove a van into pedestrians on London Bridge on Saturday night and then stabbed people in Borough Market nearby.
The Islamic State claimed responsibility for the attack, declaring that it had been carried out by “a detachment of Islamic State fighters.” It was not clear, however, whether the assailants had been trained by the militant group or if they were merely inspired by it.
As campaigning resumed around the country on Monday, the police continued to investigate associates of the assailants, whose identities are known to the police but have not been made public as the inquiry is continuing.
Twelve people were arrested in Barking, in East London, on Sunday, although one, a 55-year-old man, was released without charge. Early Monday, the police entered two other addresses in East London, one in Newham and the other in Barking, they said.
The victims of the attack are believed to have come from several countries, but only one has been identified publicly: The premier of British Columbia, Christy Clark, confirmed the death of Christine Archibald.
Four police officers were among the wounded.
Although there has been widespread praise for the professionalism and courage of the armed officers who shot and killed the assailants within eight minutes of being called Saturday night, the country’s broader antiterrorism strategy was questioned.
Opposition politicians focused their fire on Mrs. May, who gave a short speech outside her office in Downing Street on Sunday arguing that “enough is enough,” promising to shake up antiterrorism and deradicalization policies, and calling for new efforts to curb the dissemination of extremist materials on the internet.
Some of Mrs. May’s political opponents regarded her comments on Sunday as political and as a result in breach of the agreement to suspend campaigning.
Late Sunday, Jeremy Corbyn, the head of the opposition Labour Party, criticized the decrease in the number of police officers since 2010. “You cannot protect the public on the cheap: The police and security services must get the resources they need, not 20,000 police cuts,” he said.
The total number of police officers in England and Wales declined by more than 19,500 between September 2010 and September 2016, according to statistics from the Home Office. Authorized firearms officers — or armed police — declined to 5,639 in March 2016 from 6,976 in March 2010.
The government says, however, that the number of armed police is planned to increase by more than 1,000 during the next two years, that additional specialist teams are being set up outside London, and that there will be 41 additional armed response vehicles.
Mr. Corbyn also accused the government of failing to publish a report on foreign financing of extremist groups undertaken in early 2016, for fear of upsetting foreign governments.
“Yes, we do need to have some difficult conversations, starting with Saudi Arabia and other Gulf states that have funded and fueled extremist ideology,” he said. “It is no good Theresa May suppressing a report into the foreign funding of extremist groups.”
Asked by a reporter on Monday whether he would support calls for Mrs. May’s resignation over declining police numbers, Mr. Corbyn replied: “Indeed I would.”
Mr. Corbyn is also vulnerable on security issues, because of past support for Irish Republicans and because of doubts he expressed two years ago about a so-called shoot-to-kill policy for police officers during serious terrorist attacks.
Yvette Cooper, a Labour lawmaker and former chairwoman of the Home Affairs select committee, told the BBC that it was “inappropriate and wrong” to draw “precise links” between police numbers and individual attacks. But she said that fewer officers made it more difficult to gather information and to counter threats.
In a series of interviews with the news media, Karen Bradley, the culture secretary, declined to answer when challenged about the decline in the number of armed police officers in recent years. She focused instead on the need to increase cooperation with internet service providers to deprive extremists of a safe space online.
The focus on terrorism would normally be expected to help the prospects of Mrs. May’s party on Thursday, but her years overseeing antiterrorism policy present a political problem, one that has been highlighted even by former political allies.
“I am so sick of Theresa May blaming others for terror when the system she presided over has obviously failed so lamentably,” Steve Hilton, once a close adviser to Mr. Cameron, wrote on Twitter. Mrs. May, he added in a separate post, “should be resigning, not seeking re-election.”