The predictable failure of the Greek and Turkish Cypriot leaders to agree a settlement in Cyprus has thrown the burden for resolving this most unnecessary of quarrels on to the two mother countries, Greece and Turkey. Yesterday Costas Karamanlis, the newly elected Greek Prime Minister, flew to Switzerland to begin crucial talks today with Tayyip Erdogan, his Turkish opposite number, in an attempt to reach a deal that could be put to a referendum in both halves of Cyprus in three weeks’ time. If it is approved, Cyprus will enter the European Union as a united, federal country on May 1. If it is rejected, only the southern half will take up EU membership and Cyprus will have lost the best chance for a generation to resolve its bitter ethnic division.

The timetable is tight but not insuperable. Under the agreement reached at the United Nations and accepted by all sides — with varying degrees of enthusiasm — there is one further chance if the two prime ministers cannot agree by Wednesday: Kofi Annan himself will make whatever last-minute modifications necessary to the UN plan and present it as a take-it-or-leave-it ultimatum. He has already begun work in the Swiss alpine resort with his advisers, but says there will be no substantial revisions.

With luck, he may not need to intervene. Relations between Athens and Ankara have rarely been better, with Mr Karamanlis promising to continue the last Socialist Government’s conciliatory approach to Turkey. Given the emotional importance of Cyprus, there will be great pressure on him not to make too many concessions in this first test of his political mettle. But he is helped in having across the table a Turkish leader better placed to compromise than any of his predecessors. He has solid electoral support, likely to be boosted by the results of yesterday’s local elections, and is neither cowed by the powerful Army nor defiant of its role.

It is also clear that in January Ankara decided to make a strategic shift on Cyprus. The European Union will decide in December whether to open talks on Turkey’s membership application. This decision could be strongly influenced by Turkey’s readiness for a Cyprus deal. And this appears to have persuaded the Government to get tough with Rauf Denktas, the Turkish Cypriot leader, and the Army to drop its insistence on keeping a large contingent of troops in Cyprus indefinitely.

Such a shift is vital. For the blockage, all along, has been Mr Dentas. The 80-year-old has never accepted anything other than a two-state solution, and has used every political manoeuvre to sabotage any agreement. In the latest talks, he insisted on re-opening issues long since settled. But Mr Dentas is a fading force. Younger Turkish Cypriots are impatient with his intransigence. Ankara is frustrated with him. He himself has refused to go to Switzerland, sending his more pliable Prime Minister and making clear that he will campaign against any deal.

Despite genuine Turkish Cypriot misgivings, especially over fears that a mass return of Greek Cypriot refugees would overwhelm the north economically, the north is more likely to accept any deal in the referendum than the south. It has everything to gain, whereas the Greek side has a big cost to pay and is assured anyway of EU membership. The job now for Mr Karamanlis and Mr Erdogan is to find a way to persuade the reluctant Greek Cypriots that they should vote for an agreement based on the Annan plan. Without a deal soon, Cyprus will again let the best chance for a fresh start slip through its fingers. The world will then turn its back on such blinkered foolishness.