Although the letter of no confidence falls short of the 48 names required to trigger a leadership contest, the UK Parliament's summer break could prove critical for May's future as British prime minister, 'The Sunday Times' reported.
"The numbers change from day to day depending on what's happened but there are about 15 who are fairly consistent in their desire for change. If she has a quiet summer and there are no crises and things are not mismanaged then she might be able to cling on beyond conference, but that is still a big if," a former minister was quoted as saying.
"No backbiting, no carping. The choice is me or (Opposition Labour leader) Jeremy Corbyn - and no one wants him," Conservative MPs who were present reported her as saying.
Meanwhile, a Conservative party survey indicates that some Tory grassroots MPs want May to quit by Christmas time this year.
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The survey, carried out by the Party Members' Project, comes as Parliament stands down for the summer but with bitter party infighting and behind-the-scenes plotting expected to continue over the recess.
A quarter of respondentssaid they did not know or could not say who the next leader would be. However, most Conservatives are keen to avoid a leadership contest until the Brexit negotiations have concluded in 2019, and would prefer to let May finish the job - and carry the can - in the event of a poor deal with the European Union (EU).