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Shadow home secretary Diane Abbott said Mrs May, who was home secretary before becoming PM, had allowed officer numbers to fall in recent years.
The Conservatives said Ms Abbott had "dangerous" views on protecting the public.
Armed police numbers have increased, a Conservative spokesman added.
Following the London and Manchester terror attacks, security is featuring heavily in the final days of campaigning before Thursday's general election.
Labour has been targeting cuts to the Home Office's policing budget - the Conservatives have rejected the criticism and a former terrorism law watchdog said linking the cuts to terror attacks was a "completely misleading argument".
Speaking to the BBC, Ms Abbott said it was "concerning" that action was not taken when one of the London attackers - 27-year-old Khuram Butt - was known to the security services.
She said this reinforced the need for an increase in community police officers.
Latest figures show that between September 2010 and September 2016, police workforce numbers in England and Wales fell by 18,991, or 13%.
Ms Abbott said police numbers had fallen "on Theresa May's watch" despite warnings from the Police Federation and HM Inspector of Constabulary.
"So she should really consider how much of this goes back to her door and the decisions that she took," she said.
Asked how much of a connection there was between Saturday's attack and the cuts to officer numbers, she added: "She does need to explain why she thought it appropriate to watch police numbers go down by 20,000 when she had so many warnings from so many people that this was putting people at risk.
"Clearly the people responsible for these horrific terror attacks are the bloodthirsty and depraved terrorists but Theresa May has to take responsibility for letting austerity damage her ability to keep us safe."
Speaking in a special general election edition of Question Time, Lib Dem leader Tim Farron said cuts to police numbers had "not made us safer".
But Lord Carlile, the former independent reviewer of terrorism legislation, told the BBC cuts in community policing were "nothing to do with terrorism", saying "nobody in the security services is complaining about their funding"
Following the London attack, Mrs May said "things need to change" in the fight against terrorism, calling for more to be done about online extremism and for a review into whether security services needed extra powers.
Speaking to BBC Newsbeat, she defended her record, saying she had given the police extra powers to deal with terrorists and that there had been an increase in the number of people reporting suspected extremists to the authorities.
The Conservatives described Labour's criticism as "desperate stuff", saying the security services had been boosted with extra officers.
"Diane Abbott's views on keeping us safe are as dangerous as she is hopeless under pressure," a spokesman said, saying she had "voted against every piece of security legislation designed to keep us safe".