It comes amid growing concerns among Conservatives about the PM’s commitment to fully funding the UK defence sector.
One senior Tory told the Express that at least 50 fellow MPs might rebel against the autumn Budget if defence does not get £2billion a year extra to protect existing capability and fund vital modernisation.
“Defence has been cut to the bone and it’s got to stop – this is crunch point,” said the source.
Some complain that the NHS, by comparison, will get an extra £20billion a year – despite failing to make efficiency savings.
One said: “People are saying what’s the point of keeping everyone healthy but not worrying about them dying at the hands of an enemy.”
But others hope the PM will pledge extra cash at July’s Nato summit.
Mr Williamson is said to have told service chiefs at a meeting he would “crush” the Treasury in his fight for more funding.
And asked if Mrs May would back him, the former Chief Whip who ran her campaign to be PM, allegedly declared: “I made her – and I can break her.”
Mr Williamson has support from some colleagues, such as defence select committee chairman Julian Lewis, who said: “There need be no political risk to the PM – if she does the right thing.”
But others were angry, saying MPs had been lobbying to prevent further defence cuts.
One said: “But there’s no way we’d break cover now to back this weasely attack on the PM.”
One said: “Threatening the Treasury and the PM is not a very clever way of getting what you want.”
However, one source defended Mr Williamson, saying it was “absurd and completely unfounded to suggest he was behind a plan to bring down the PM – though he was aware of the strength of feeling among MPs”.
Meanwhile, Treasury chief secretary Liz Truss will issue a warning to Mr Williamson and other ministers when she says in a speech tomorrow it is “not macho” just to demand more money and the “tougher skill” is to insist their departments spend existing budgets more efficiently.