Boris Johnson goes to Chequers for Sunday lunch Europe is a particularly sensitive issue. Mr Johnson backs demands for an "in/out" referendum on Britain's membership of the European Union, while Mr Cameron has so far resisted pressure form his party to promise one. He has, however, suggested that a vote could be held at some stage after the next general election in 2015. Mr Johnson has also clashed with Mr Cameron over airports in the South East, urging the Prime Minister to "stop pussyfooting around" and increase capacity. The Mayor favours building a brand new airport in the Thames Estuary, dubbed Boris Island. This month, Mr Johnson also intervened after Andrew Mitchell, the chief whip, had an angry altercation with police guarding Downing Street in which he was accused of calling officers "plebs." The Mayor said the police would have shown "common sense" if they had arrested the Chief Whip. Mr Cameron has refused calls to order an inquiry into the incident. Mr Johnson constantly denies he has ambitions to succeed Mr Cameron. Some Tories, however, want him to try to return to parliament before the 2015 election so that he would be able to launch a challenge for the leadership. His term as mayor only ends in 2016 - but Labour's Ken Livingstone set a precedent by occupying both a Commons seat and the top London job in the 2000s. On his trip to Brazil last week Mr Cameron was asked by an interviewer if he felt threatened by his fellow Old Etonian. Some at No10, however, believe Mr Johnson wastes no opportunity to try to upstage Mr Cameron, citing the parade of Britain's Olympic athletes in London this month. Addressing crowds in the Mall he told them the Games had come to "final tear-sodden juddering climax," while the Prime Minister was more measured, telling athletes: "You showed us the best face of Britain." Although Chequers has a tennis court, where the Prime Minister has taken on, and beaten, Nick Clegg, it was not known whether he would challenge Mr Johnson there. The two men last clashed in a wheelchair tennis match last year to promote the Paralympic Games - a contest won by Mr Johnson.