Theresa May has decided to commit billions of pounds on preparing Britain to leave the European Union without a deal in a bid to save her premiership.

The spending, which will be “unlocked” in the new year if no progress is made with Brussels, is intended to send a signal to pro-Brexit MPs that she is serious about regaining the upper hand in the negotiations.

It came as rebel MPs gave Mrs May until Christmas to make real progress on Brexit to avoid another attempt to oust her.

One group of rebels, led by former chairman Grant Shapps, said they had not been appeased but would wait before attempting to prise Mrs May out of 10 Downing Street.

Key figures who loom as possible replacements for Mrs May – Boris Johnson and Amber Rudd – were said to be “biding their time”, while an ally of David Davis said Mrs May had one disaster left “before she falls”.

As part of a rearguard action to save Mrs May:

Boris Johnson, the Foreign secretary, said in a Telegraph article that Tory rebels who wanted to unseat the Prime Minister were “nutters” but admitted that MPs had “sniffed the air” before deciding to back Mrs May;

The Midlands Industrial Council, which represents the party’s largest donors, issued a statement backing the Conservative leader and held out the prospect of withdrawing funds from Tory MPs who tried to unseat her;

Tory grass roots campaigners told plotting Conservative MPs that “these petty and childish games only act as a distraction and are opposed by ordinary party members”;

Two Conservative MEPs were stripped of the party whip after supporting a resolution in Brussels to block Brexit talks moving forward.

The Telegraph can disclose that Philip Hammond, the Chancellor, is planning to sanction the Brexit spending in the new year to prepare the UK for leaving in March 2019 without a deal with the EU.