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In the wake of three terror attacks in three months, the Labour leader attacked Mrs May over government cuts which has left the police with 20,000 fewer officers than in 2010.
Mr Corbyn conceded that Thursday's general election was "perhaps the best opportunity" to remove the PM from her post, but asked by ITV News if he backed calls for Mrs May to resign, he said: "Indeed I would, because there's 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 is now saying that we have a problem - yes, we do have a problem, we should never have cut the police numbers."
Mrs May has refused to say whether cuts to police numbers under her watch should be reversed after the head of the Metropolitan Police called for more resources in the wake of the London Bridge attack.
The prime minister was repeatedly challenged over her record as home secretary when she presided over cuts that have seen 20,000 fewer police officers on the country's street.
Met Police Commissioner Cressida Dick said "we need to look at our resourcing" in response to the emerging terrorism threat.
At an election campaign event in London, Mrs May said: "Cressida Dick has said that the Metropolitan Police are well resourced - and they are, she has said they have very powerful counter-terrorism capabilities - and they do.
"We have protected counter-terrorism policing budgets, we have funded an uplift in the number of armed police officers."