David Cameron has denied he is a jinx for England sports teams, after the rugby union, cricket and football teams each crashed out of world cups in the group stages in quick succession.

The Prime Minister said claims of a "curse of Cameron" annoyed him, and pointed to successes in the Olympics and the cricket Ashes against Australia which had happened under his premiership.

Mr Cameron refused to say whether he thought England rugby head coach Stuart Lancaster should be sacked after his side's elimination from the World Cup on home soil.

In an interview on LBC radio, the PM was asked by host Nick Ferrari whether there was a "curse of Cameron" affecting English teams.

He replied: "That annoys me so much. That's nonsense. Who was Prime Minister this summer when we won the Ashes, thank you very much? I was Prime Minister when we had the best ever haul of Olympic medals.

"I always support England and we don't always win. Shock, horror, surprise.

"I shouldn't let these things annoy me but I was there on the great night when Mo Farah won gold twice. I've witnessed some great sporting triumphs.

"There is no curse. It's probably the curse of Ferrari."

Speaking at the Conservative conference in Manchester, Mr Cameron said that since England were knocked out of the rugby tournament, he had been supporting the other home nations.

"I've been going round this conference and I went to the Northern Irish fringe meeting, the Scottish fringe meeting and the Welsh fringe meeting and at each one I said 'At 10 o'clock on Saturday night, I became a Welsh or an Irish or a Scottish rugby fan'," he said.

Pressed on whether Lancaster should go, he replied: "Not a matter for me. I appoint my Cabinet, somebody else appoints the head of English rugby football. I know how sad the team must be."

And he revealed that both he and London Mayor Boris Johnson were keen rugby players in their youth, though they did not play in sides together in their time at Eton College and Oxford University.

"Boris was a very good tight-head prop, I think, and he likes rugby analogies," said the PM. "I don't know whether he still plays.

"I was a flanker. Hard to believe. I was tiny, wee, when I was 13.

"He was a very good rugby player and I was mediocre. Now we are bound together as if in a scrum, pulling in the same direction, the ball at our feet."