At a fundraiser last Thursday, around a quarter of the 50 Conservative financial backers present called for her resignation, according to one donor at the meeting.
This unrest comes as the Prime Minister meets with her Cabinet this morning to thrash out a position on exactly what the Government hopes to achieve from Brexit.
Several senior ministers, including Foreign Secretary Boris Johnson, are pushing for a clean break from Brussels.
But others, such as Chancellor Philip Hammond, have expressed their desire to see a soft Brexit with minimal changes to the current arrangement.
The fundraising dinner in London saw several “very, very traditional donors” question Mrs May’s leadership, according to The Times, which reported a donor as saying: “Among even the most loyal middle-ranking donors there is utter despair.”
The attendee said Dominic Johnson, who is a Tory party treasurer, stood up and asked the room: “I love Theresa May. Who could possibly want to replace her?”
About a quarter of the donors then replied they wanted to see the PM step down.
In addition to a revolt by party donors, Mrs May is potentially facing a vote of no confidence from her own backbenchers.
Sources have revealed around 40 Conservative MPs have formally submitted letters to the party’s powerful 1922 Committee calling for a change in leadership.
If 48 letters are submitted, the committee’s chairman Sir Graham Brady will be obliged to launch a leadership contest.
However, a number of senior Tories have rallied round Mrs May, insisting a change in leadership at such a crucial time in the Brexit process would destabilise the Government and only serve to increase the chance of Jeremy Corbyn’s Labour winning power in the next election.
Calling for calm yesterday, Culture Secretary Matt Hancock urged fellow Tory MPs to “pull together and pull behind the Prime Minister”.
He told the BBC’s World at One: “There are challenges facing the country that we need to rise to together, there’s also some huge opportunities that we need to take advantage of.
“The biggest risk to our country would be a socialist government that would send us backwards and would undermine all of the work that we have done to get the economy going – with a record number of jobs – and in a whole host of areas where we have made progress.”
However, the PM faced criticism from a number of her own MPs, including former minister Nicky Morgan who said Mrs May’s Cabinet needs to “get a grip” and make a “realistic” decision on what the UK hopes to achieve from Brexit.
Writing in a blog post for ConservativeHome website, Mrs Morgan said: “There were times last year for the Prime Minister to step aside – immediately after the June 2017 election, or after Party Conference.
“That didn’t happen. Maybe the Cabinet should have asked her to go, but they didn’t.
“We are now into a critical nine months for the future of the country, so the Cabinet need to get a grip by acting collectively to shape Brexit and agree an ideal end-state based in reality, on what Parliament will approve eventually – and then stick to it.”