Jeremy Corbyn, the leader of the opposition Labour Party, when asked by a reporter if he would support calls for Mrs. May’s resignation over the falling number of police officers, replied, “Indeed, I would.”
Stung by the criticism just days before a critical national election on Thursday that will decide her political future, Mrs. May responded at a news conference. “We have protected counterterrorism policing budgets,” she said. “We have also provided funding for an increase in the number of armed police officers.”
She cited comments from Cressida Dick, head of the Metropolitan Police in London, that the city’s force is well resourced and has powerful counterterrorism abilities.
When pressed by reporters, the prime minister also came to the defense of Sadiq Khan, the mayor of London, who was mocked by President Trump over his response to the attack.
A focus on security would normally be expected to help the prospects of Mrs. May’s Conservative Party in the coming general election.
But as the investigation builds, so does speculation of potential security lapses that could have been prevented, possibly along with Saturday night’s attack.
The Metropolitan Police released photographs on Monday of two of the assailants they shot dead, saying that one of them was known to the intelligence services.
In a statement, they said they believed one of the suspects was Khuram Shazad Butt, 27, a British citizen who was born in Pakistan and known to MI5, the agency that deals with internal security.
The other man was identified as Rachid Redouane, 30, who had claimed to be Moroccan and Libyan but who had also used the name Rachid Elkhdar and a different date of birth.
“Khuram Shazad Butt was known to the police and MI5,” the statement said. “However, there was no intelligence to suggest that this attack was being planned, and the investigation had been prioritized accordingly. The other named man, Rachid Redouane, was not known.”
Work is still underway to identify the third man who was killed during the attack on Borough Market.
The statement added that “work is ongoing to understand more about them, their connections and whether they were assisted or supported by anyone else.”
Both of the men identified as attackers were from Barking, in East London, where 12 people were arrested on Sunday, although one, a 55-year-old man, was released without charges. Early Monday, the police raided two other homes in East London, one in Newham and the other in Barking.
The main political parties suspended campaigning on Sunday as a sign of respect for the seven people killed and the scores wounded in the attack, but as campaigning resumed on Monday, so did the pressure on Mrs. May.
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 on Downing Street on Sunday saying 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 as political and, as a result, in breach of the agreement to suspend campaigning.
Late Sunday, Mr. Corbyn criticized the decrease in the number of police officers since 2010. “You cannot protect the public on the cheap,” he said. “The police and security services must get the resources they need, not 20,000 police cuts.”
The total number of police officers in England and Wales fell more than 19,500 from September 2010 to September 2016, according to the Home Office. Authorized firearms officers — or armed police officers — declined to 5,639 in March 2016 from 6,976 in March 2010.
The government says, however, that the number of armed officers is to increase by more than 1,000 in 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, undertaken in early 2016, on foreign financing of extremist groups, for fear of upsetting foreign governments, although he himself is vulnerable on security issues.
Mr. Corbyn has demonstrated past support for Irish republicans and expressed doubts two years ago about a so-called shoot-to-kill policy for police officers during serious terrorist attacks.
Four officers were among the wounded in Saturday night’s attack. The victims are believed to have come from several countries, but only one has been identified publicly: The premier of British Columbia in Canada, Christy Clark, confirmed the death of Christine Archibald.
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.
Despite the sniping between Britain’s two major parties, Mrs. May had praise for one prominent Labour figure — Mr. Khan.
Asked at the news conference about a tweet from Mr. Trump that was critical of Mr. Khan, Mrs. May said she was working closely with the mayor and that he was doing “a good job,” adding, in answer to persistent questioning, that it was “wrong to say anything else.”
The dispute began when President Trump commented on Twitter with a post suggesting that Mr. Khan was minimizing the threat in London, but he appeared to misrepresent what the mayor had written.
A spokesman for Mr. Khan, in response, said on Sunday that the mayor had “more important things to do than respond to Donald Trump’s ill-informed tweet that deliberately takes out of context his remarks.”
On Monday, President Trump fired back on Twitter, aiming at both the mayor and the mainstream media.
Tim Farron, leader of the Liberal Democrats, described President Trump as “an embarrassment to America,” and he called on Mrs. May to cancel his planned state visit to Britain.