The Prime Minister and Lynton Crosby, the communications expert drafted in by the Tories, warned them to be careful in how they use Twitter at a meeting of backbenchers at Westminster.

Earlier, Education Secretary Michael Gove had reportedly warned senior figures who promoted their leadership credentials were playing into the hands of the Tories' opponents.

Mrs May fuelled rumours she is positioning for a post-Cameron era by delivering a wide-ranging speech at the weekend.

Pressure has been mounting on Mr Cameron to adopt right-wing policies after the Eastleigh by-election.

Defence Secretary Philip Hammond also took negotiations over the 2015-16 spending review public by calling for deeper cuts to welfare.

Mr Crosby is said to have reminded MPs they were "participants not commentators" and urged them to focus on welfare reform and the in-out EU membership referendum pledge, both issues where the Tories poll strongly against Labour.

He said they must stress the next election would be a choice between Mr Cameron and Labour leader David Miliband as prime minister.

Meanwhile, George Osborne said his Coalition colleagues have until June 26 to make the case against departmental budget cuts further in 2015/16 amid fears of a triple-dip recession.

The Chancellor needs to find another £10 billion of cuts for the year after the next General Election but schools, hospitals and overseas aid are protected.

Yesterday, Mr Osborne said he would publish his spending review on that date.