The venue couldn’t be more neutral – or more resonant. Nicosia Airport is within the UN-supervised no man’s land that bisects the island, the dilapidated Trident jet on the tarmac a ghostly reminder that this once thriving eastern Mediterranean hub has been disused and out of bounds since the war of 1974.

An apt setting, therefore, for today’s summit meeting at which the President of Cyprus, Nicos Anastasiades, and his Turkish Cypriot counterpart, Mustafa Akinci, will try to advance the process of finally reunifying their divided country.

Will their efforts succeed where all the others have failed? And can they achieve a settlement acceptable to the Greek Cypriots, 72 per cent of whom rejected in a 2004 referendum the last concerted effort – the UN-sponsored Kofi Annan plan – to forge a new Cyprus from its two parts as a “bi-zonal, bi-communal federation”.

There are tentative grounds for thinking they might succeed, not least the relationship between the two men. Although a right-winger, Mr Anastasiades voted for the Annan plan in 2004. And he now has a Turkish Cypriot partner who is at least as committed to finding a solution. The leaders, both in their late sixties, have in common an upbringing in the port of Limassol; Mr Akinci was among the 17,000 Turkish Cypriots who left in 1974 and moved to the north.

A significant step came in the celebrated battle for EU protected designation of origin (PDO) status for halloumi cheese – hellim in Turkish – as uniquely Cypriot, when the two men agreed that an independent agency should monitor the quality of the cheese. Because of mutual non-recognition, inspectors working for the Greek Cypriot Republic of Cyprus could not have done the job.

As a former mayor of the northern part of divided Nicosia, Mr Akinci joined with his then Greek Cypriot counterpart – Lellos Demetriades – to fix the city’s broken sewerage system. The two mayors then produced a Nicosia master plan that can only be fully implemented in a reunited Cyprus but which is already having practical effects within the capital’s old city.

The pedestrianised Ledra/Lokmaci St is again a single thoroughfare, save only for the boarded-up shops in the UN buffer zone and the two passport control points.

Beside their formal meetings and a much-photographed glad-handing session at a northern Nicosia café earlier this summer, Mr Akinci will take the powerfully symbolic step of joining Mr Anastasiades in opening an exhibition devoted to the late Greek Cypriot President Glafco Clerides at an arts centre in southern Cyprus. Beside housing a stunning collection of foreign artists’ work in Cyprus spanning three centuries, the centre is about to run ground-breaking free courses for schoolchildren from both north and south.

Greek Cypriot leaders have interpreted Mr Akinci’s 62 per cent election majority in April as confirming Turkish Cypriots’ support for a peace-seeking leader who might be less beholden to Ankara than his hawkish predecessor, Dervis Eroglu.

The message, Greek Cypriot Foreign Minister Ioannis Kasoulides told The Independent, was that Turkish Cypriots were willing to work with their Greek Cypriot counterparts “for the interests for Cyprus in a spirit of Cypriotness, instead of depending on others”. All seven meetings between the leaders “have produced progress”, he said, adding: “I have never seen in the past negotiations advancing in such a way.”

Which doesn’t make it easy. The self-proclaimed Turkish Republic of Northern Cyprus – recognised only by Turkey – occupies about a third of the island. But while its territory would be reduced in any new federation, the precise boundaries would depend on the burning issue of properties abandoned in 1974. That was when the Turks invaded Cyprus, in response to the dispatch by the Greek military junta of troops seeking to enforce the demand of militant Greek Cypriots for “enosis” – incorporation into Greece.

Some 160,000 Greek Cypriots fled their northern homes, most of which are now occupied by Turkish Cypriots and Turkish incomers. Resolving the issue – high on today’s agenda – is likely need a combination package in which some Greek Cypriot refugees return to the north, some do house swaps with Turkish Cypriots who left the south in 1974, and some are paid compensation.

Nor will Greek Cypriots accept the continued presence of 35,000 Turkish troops in the north. While the newly independent Cyprus’s 1960 constitution provided for 950 Greek and 650 Turkish troops, Greek Cypriots want none at all. “What solution are we talking about when we need Turkish troops in any number – or Greek troops – on this island?” asks Mr Kasoulides. Instead, the two sides should opt for a “totally independent” state “with all the Cypriots working for the interests of Cyprus”, he said.

What was more, as the EU’s most easterly member, Cyprus needed a “totally independent” foreign policy, he said. “I don’t think even the best allies of Turkey want to see a foreign policy of Cyprus similar to the one that took two years for [the Turkish air base of] Incirlik to be used … against Isis.”

Nor do Greek Cypriots want retention of the security “guarantee” that Turkey, along with Britain as the former colonial power, and Greece, enjoyed under the 1960 constitution. The 1974 Turkish invasion, although initially justified as application of the guarantee because of Greece’s military intervention, led to half a century of what Greek Cypriots see as foreign occupation.

Then there are “settlers” from Turkey, encouraged by Ankara, deeply resented by Greek Cypriots – and increasingly resented among the 120,000 Turkish Cypriots whom the settlers now outnumber. Settler citizenship remains an issue.

Political equality is especially important to Turkish Cypriots, however. Because of their larger population, Greek Cypriots might hold a rotating federal presidency perhaps two years in three. But in years allocated to a Turkish Cypriot president, his compatriots would have a “weighted” vote to prevent the Greek Cypriot majority effectively choosing the Turkish Cypriot president. Equally, Greek Cypriots returning north would still vote only in their own, southern, federal district.

The key to success in all this could be Turkey itself. Mr Kasoulides says cautiously that he has no evidence so far that Turkey is seeking to “dictate” positions to Turkish Cypriots, and points to Ankara’s public encouragement of negotiations. But the key issues for Turkey of an agreed new territorial map and the security guarantee have not been reached, Mr Kasoulides says, and Turkey has yet to show its hand. “We are not discussing these two issues yet,” he said. “They say that they’re interested in a solution… Now is the time when words have to go along with deeds.”

That said, Turkey is said to have indicated privately that it would not insist on the guarantee, if Turkish Cypriots asked it not to.

Turkish President Recep Tayyip Erdogan could even be more willing to sanction a solution than the Turkish militarist “deep state” whose influence he has sought to overcome. Conversely, prominent Greek Cypriots believe that Mr Akinci’s eagerness for a deal is underpinned by impatience among many Turkish Cypriots with the “Islamification” imported by settlers from Mr Erdogan’s AKP-led Turkey. “The Turkish Cypriots are more secular than we are,” said one, only half-jokingly referring to his own Greek Orthodox community.

On the economic benefits of a deal, Mr Kasoulides is firm. “Put yourself in a position of an investor,” he said. “You see a potential from … the period of opportunity after reunification.” He argues that tourism would benefit hugely – not least from rehabilitating the Varosha suburb of Famagusta, Cyprus’s number one holiday destination until its seizure by the Turks in 1974, and still a closed Turkish military zone.

Reunification would also enable trade with Turkey – not least, officials say, because of the discovery of natural gas off the coast. Gas from a reunified Cyprus could reach European markets through a pipeline to Turkey – a boon to both.

Mr Kasoulides says there were “difficult issues” for public opinion, but that “circumstances are better” than during the rejected UN deal in 2004. First, many Greek Cypriots saw the Annan plan as externally imposed. This time, a solution will have emerged from the island itself. In 2004, moreover, the then Greek President Tassos Papadopolos recommended a “no” vote. “This time nothing will be presented to the people unless it is agreed by the two leaders,” Mr Kasoulides said.