The prime minister’s hopes of securing a swift EU renegotiation were hanging by a thread last night after the president of the European Council walked out of Downing Street, declaring “no deal”.

Donald Tusk, a former Polish prime minister, arrived at the critical dinner saying that he would put forward an outline deal as soon as today if progress were made, but he left only an hour and 45 minutes later.

His abrupt departure, and brusque reply to reporters outside, led one former cabinet minister to declare that Britain was heading out of the EU. In fact, David Cameron has been given 24 hours to strike a deal on his preferred timetable, under which a referendum would be held in June on whether Britain should