As backbenchers express increasing confidence that David Cameron will face a challenge to his leadership later this summer, the home secretary will on Saturday set out her views at a conference organised by the ConservativeHome website.
The speech by May, who has been leading calls by a group of cabinet ministers known as the national union of ministers against further cuts to their budgets, follows a series of carefully calibrated interventions to burnish her credentials on the right. Earlier in the week the Daily Mail reported that the home secretary was planning to impose a financial bond on some immigrants.
One senior Tory said: "When you are halfway through a parliament there is a natural tendency for people to start positioning themselves. I do not under estimate the ambitions of Theresa May."
But a leading rightwinger detected the hand of the chancellor under pressure from the so-called national union of ministers. This group, led by the home secretary with support from the defence secretary, Philip Hammond, is attempting to focus future spending cuts away from departments such as the Home Office and the Ministry of Defence. The MP said: "George is clearly encouraging speculation about Theresa and Philip. It disables them."
May was thrust into the spotlight this week when Ed Miliband made light of her apparent leadership ambitions during prime minister's questions when she sat next to Hammond. The home secretary gave Miliband a thunderous look when he said: "I am looking forward to facing her when they are in opposition."
The speculation about May has been prompted by a growing belief among some backbenchers, as the Guardian revealed last weekend, that the prime minister will face a vote of no confidence later in the summer if the chancellor fails to inspire confidence in the budget and the Tories perform poorly in the local elections in May.
A vote will be triggered if 46 Tory MPs write to Graham Brady, the chairman of the backbench 1922 committee. "It is surprising how widely the unease is spreading," one MP said.
Tory MPs have mixed thoughts about May. She is said to be modelling herself on John Major, who carefully and surreptitiously positioned himself to succeed Margaret Thatcher by reaching out to the right. One MP said: "Theresa is clearly serious about it. But she is not a leader. She is a loner. She works very hard. She is clearly a good home secretary. But she is not a leader."
One well-placed Tory was scornful of May's so-called "submarine" strategy, in which she adopts a low media profile and surfaces at times of her own choosing. "It's not much of a submarine strategy if we are all talking about it," the MP said. "I think Theresa's submarine must have a defective sonar."
Another MP thought a telltale sign was May's decision not to dampen speculation about her leadership intentions. The MP said: "If Theresa thought all this was ridiculous she could say it's all daft and there is no vacancy. But nobody in her team has done that."
Others say the speculation about May has been prompted by the tactics of her parliamentary private secretary, George Hollingbery, who replaced Edward Timpson when he was appointed children's minister. Hollingbery, a millionaire who has put his north Cornwall cottage at the disposal of David Cameron's family, has run a more political operation for the home secretary.
"George has made a simple calculation," one MP said of Hollingbery, who is a member of the executive of the 1922 committee. "He knows that the job of a home secretary involves permanently crossing a minefield where you never know if it is going to blow up in your face. She therefore needs to have good links with the backbenches and will do herself no harm if she tacks to the right. George has been instrumental in all of that because he is a little more worldly than Edward."
Another MP said: "Is George plotting to ensure Theresa May is replacing David Cameron? No he is not. Is he thinking that his star could rise with Theresa's in the future? Of course he is."
The speculation about May comes as the Tory right plans to intensify the pressure on No 10 by demanding that the prime minister issue an immediate challenge to the Liberal Democrats on an early EU "mandate" referendum. This would be an initial referendum to give the prime minister a mandate to negotiate a change in the terms of Britain's membership of the EU. This would then be followed be a "decision" referendum.
Senior MPs are to tell Cameron, who is delaying a referendum until after the next general election, that he should table legislation for an early referendum. "If anyone doesn't like it they should resign," the Tory said of the five Liberal Democrat cabinet ministers, led by Nick Clegg, who are opposed to a referendum.
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