A former Cabinet minister claimed “negativity” at the top of the Government was hampering the departure, while a leading Tory donor called for the Prime Minister to be replaced by Michael Gove.
Also, a survey yesterday showed nearly two-thirds of Tory activists had no confidence in her leadership in the Brexit negotiations.
The row over Europe deepened when a “Doomsday” warning about the possible consequences of Britain quitting the EU without a deal was leaked by Whitehall.
The document, drawn up by civil servants for Brexit Secretary David Davis, claimed the UK would be hit by shortages of fuel, medicine and food within a fortnight.
It also said the port of Dover would collapse on the first day of a no-deal Brexit.
Brexit-backing Tories were furious about the claims last night.
Senior backbencher Jacob Rees- Mogg said: “Project Fear was wrong, is wrong and will be wrong.”
Andrew Bridgen, another senior Tory MP, branded the document “a sequel to Project Fear”, adding: “Each remake of this tired format becomes more ludicrous and less convincing.”
A spokeswoman at the Department for Exiting the EU said: “These claims are completely false. “
A significant amount of work and decision making has gone into our no-deal plans, especially where it relates to ports, and we know that none of this would come to pass.”
The row erupted after former international development secretary Priti Patel launched a scathing attack on the Government.
She admitted to being concerned that Mrs May and Chancellor Philip Hammond, who both backed Remain, were the two most senior gures in a Government negotiating departure from the bloc.
“There is absolutely something in that,” she said in an interview with the Parliamentary magazine The House.
“We hear marginal noises from only a couple of key Brexiteers in Government but where are the others? We need to hear stronger advocacy. We need to hear a better vision for the future.”
Ms Patel also complained that the Tories were at risk of abandoning their position as the party of “meritocracy”.
Ms Patel said: “I’m a proud Thatcherite because she was in tune with the hopes and aspirations of the British public. Meritocracy, political and economic freedom – those should be the DNA of the Conservative Party.
“Quite frankly, I don’t see much of that going on right now.”
Crispin Odey, a hedge fund manager who backed the Leave campaign in the EU referendum, said Mr Gove had the right skills to make a success of Brexit.
Mr Odey, who gave £50,000 to the last Tory general election campaign said: “There’s no point in voting for freedom if you don’t know what to do when you’re free.
“What is true is that you have a whole lot of people who didn’t want this to happen who are in charge of it happening. I would go to Gove. He’s the only minister who is still being a minister.”
A survey by the Conservative Home website for Tory activists found 63 per cent of respondents had “no confidence in the Government’s handling of the Brexit negotiations”.
Only 28 per cent of those who answered the survey disagreed.
A Downing Street spokesman said: “The Prime Minister has been clear that we are leaving the single market and the customs union and want to build a new relationship with the EU, one that ensures the British Government is in control of our laws, our immigration policy and how taxpayers’ money is spent.”