The Tory Brexiteer accused Mrs May of a “catastrophic misreading” of public opinion, and was now little more than a caretaker leader.
His comments come amid mounting pressure on Mrs May.
Mr Paterson said Mrs May’s resignation was now the only way the Brexit deadlock could be broken, adding that the stalemate had brought the business of government to a standstill.
He said the House of Commons was now regularly finishing in mid afternoon because there was nothing for MPs to discuss.
“This paralysis is the result of the barely believable intransigence of a Prime Minister consumed by the increasingly deluded aim of passing an agreement which MPs have thrice told her in emphatic terms is a bad deal.
“Her response each time has been unmoved: ‘Pass my deal’.
“Her response to every Brexit question before the liaison committee last week amounted to: ‘pass my deal’. Her response to the local elections which saw 1,330 Conservative Councillors unseated and 44 Conservative Councils lost has been: ‘pass my deal’.
“This is a catastrophic misreading of public and Parliamentary opinion. Yet in pursuit of her hopeless aim, the Prime Minister has broken almost every promise she has made and reduced herself to a caretaker.”
Telford MP Lucy Allan also said it was time for Mrs May to go.
“Theresa May has done all she can in the Brexit negotiations but has been unable to bring about our exit from the EU,” she said.
“I don’t believe that any further attempts to bring back her withdrawal agreement will succeed.
“It is therefore time for her to step aside and for a new leader to adopt a different approach. She failed to take the UK out of the EU on 29 March, put simply her Brexit plan has failed. The Prime Minister has fought tirelessly in the most difficult circumstances. A Remain dominated Parliament, many of whom refuse to accept the referendum result and an intransigent EU have made her job that much harder.”
She said the European elections should not be taking place, and many voters would use the election to protest at the failure to deliver the referendum result.”
However, Shrewsbury & Atcham MP Daniel Kawczynski said now was not the time to get rid of the PM, warning that it could delay Brexit once more.
“It’s extremely important this last-ditch attempt at getting a cross-party agreement is given a chance, she should at least be given the chance to do that,” he said.
“I understand she could be bringing an agreement back before the house, certainly before the European elections. She has worked hard on this, and should be given that opportunity.”
Mr Kawczynski said it was down to “recalcitrant” members of the European Research Group (ERG) – which he recently left – that Britain had not left the EU.
“I think the people of Britain need to know the Members of Parliament who have continued to obstruct and vote against the withdrawal agreement,” he said.
Glyn Davies, MP for Montgomeryshire, said the calls for Mrs May’s resignation were unhelpful.
“The Prime Minister has already announced she’s not fighting the next election, and all these calls for her to resign are not helpful to the Conservative Party, and they are not helpful to the country,” he said.
“I just think they should stop it. Anybody who calls for the Prime Minister to go sacrifices my support.”
Mark Pritchard, MP for The Wrekin, declined to be drawn on whether it was time for Mrs May to go. But he added:
“The PM must listen to what people are saying.”
Ludlow MP Philip Dunne said Mrs May had his support.
“She has said she intends to step down, and it needs to happen in an orderly way, but I’m not going to get drawn into when or how it should happen,” he said.