That was a far-from-subtle reminder of Mr Cameron’s still contentious decision to end the Conservatives’ traditional backing for grammar schools.

Mr Johnson was addressing a rally of almost 1,000 Tory members who cheered his arrival and applauded a performance that also took in aviation policy, an economic recovery and the “terror” of French tax rates.

The speculation around Mr Johnson’s ambitions – and what many see as his failure to end it – has angered some Conservatives, especially those close to Mr Cameron, although Downing Street says the Prime Minister is relaxed about the mayor’s popularity.

In his Daily Telegraph column on Monday, he suggested that the middle classes were being ignored under the Coalition.

Kenneth Clarke on Monday told Mr Johnson to “calm down” and suggested he was courting publicity.

On Monday night, at a meeting about the London 2012 Olympics Mr Johnson insisted that talk of his prospects was a media creation. “No one should have any reason to doubt my admiration for David Cameron,” Mr Johnson said.

“In tough circumstances, he, George Osborne and the rest of the Government are doing exactly what is needed for this country.” He will repeat that support today in his main conference speech.

But last night, Mr Johnson put himself at odds with his leader again, saying: “We should be able to allow children to compete academically.”