Cabinet ministers must “step up” to oust Theresa May in order to rescue Brexit and prevent Parliament taking control, senior Tories have warned.

Nicky Morgan, the pro-EU former education secretary, said that members of the Cabinet must now tell Mrs May “it’s time to go”. Steve Baker, a leading Brexiteer, said would-be leadership contenders around the top table must “act now” if they wanted to persuade MPs that they were “the great statesmen to take us forward”.

The ex-ministers broke cover as growing numbers of Tories privately and publicly said that the Prime Minister should leave Downing Street, or at least cede control of Brexit to senior ministers. Under one plan discussed by Remainer ministers including Amber Rudd, David Lidington, the pro-EU de facto deputy prime minister, would take over as a “caretaker” leader, possibly with a Brexiteer such as Michael Gove as chancellor.

But another senior minister warned that such a plan would be intended to “kick the can down the road yet again in the hope that something will happen to stop it”.

The People’s Vote campaign has claimed more than one million people attended a march in London calling for a second referendum.