Boris Johnson, the foreign secretary, will lead the UK delegation to the Cyprus peace talks in Geneva on Thursday, but if the talks go well it is possible Theresa May will also attend alongside the Turkish president, Recep Tayyip Erdoğan, and the Greek prime minister, Alexis Tsipras.

Britain is critical to the talks on future security guarantees for the former British colony in the event of an agreement on other issues such as political equality, future boundaries and compensation.

Britain’s prime minister spoke with Tsipras last week, and on Saturday with Erdoğan. Following the Erdoğan call, May’s office said the talks were “a real opportunity to secure a better future for Cyprus and to guarantee stability in the wider region”.

May has kept in close touch with the talks process, seeking detailed memoranda from officials, but will only travel to Geneva if it is thought her presence could help clinch a framework agreement, the most British officials expect from the three-day meeting.

It would be a considerable feather in May’s cap if she was able to help preside over a peace settlement in the eastern Mediterranean, as the island has been afflicted by inter-communal tension ever since its independence from the UK in 1960.

Successive prime ministers and UN secretary generals have seen a peace deal elude them, most recently in 2004 when the then UN secretary general, Kofi Annan, saw his plan accepted in Turkish northern Cyprus before being heavily defeated by a referendum in Greek Cyprus.

Britain regards an agreement as critical not just to end a 43-year post-colonial conflict, but also to improving wider Greek-Turkish cooperation on migration in the region.

An option exists for the Geneva talks to reconvene perhaps in a couple of weeks, but the British, along with the EU and UN, will be pressing the Turks and Greeks at least to reach a conclusion since the window for a referendum on the framework reunification agreement is relatively narrow.

The Greek-Cypriot government faces elections next year, and a referendum as early as April is feasible.

The UK, one of the three guarantor powers under the 1960 Zurich agreement that granted Cyprus independence, recognises that the outcome of the talks is highly unpredictable, and even the makeup and status of the delegations is up for discussion.

In the peace talks led by Annan in 2004, the UK offered to relinquish 49% – or 117 sq km (45 sq miles) – of the territory its sovereign military bases hold in Cyprus, and the UK has repeated the offer in the hope that the release of land will make it easier for the Greek Cypriots and Turkish Cypriots to reach an agreement on land swaps.

A Tornado jet lands at RAF Akrotiri in Cyprus. Britain has offered to give up 49% of the territory its military bases hold on the island. Photograph: Nick Ansell/PA

The remainder of the military base – critical as an intelligence listening centre and much prized by the Americans – is not up for discussion in the talks, as the British claim the UK sovereignty of the base was agreed in the treaty founding Cyprus. British officials are confident that the issue of the British bases will not be raised at the summit.

But the future role of the UK as a security guarantor for the island will be at the heart of the talks.

The UK has said it is willing to be flexible about relinquishing this role if the other parties seek this. At present the UK, Turkey and Greece are guarantors, alongside a UN peacekeeping presence. But the Greek Cypriots would prefer the security guarantor role be handed to the EU now Cyprus is a member state. It is argued that the individual rights of Turks on the island are best protected through the European court of justice and a balanced constitution.

So far the Turkish Cypriots have insisted Turkey must remain as a guarantor. It is possible Britain could offer it a greater role in the UN peacekeeping force.

Turkey has about 30,000 troops on the island, and no deal is likely unless the unpredictable Erdoğan agrees to a Turkish timetable for their drawdown and a pact on non-interference. Russia, increasingly close to Turkey on foreign policy, has argued that Britain should abandon its guarantor status, along with Greece and Turkey.

The UK has been probing the Turks on security guarantees, but it is likely Erdoğan will wait for offers made on land swaps, compensation, political equality and EU funding.

The Turkish prime minister, Binali Yıldırım, said last month: “If there will be a solution in Cyprus, it must be a solution based on a just administration, a rotating presidency under which the rights of both people and property are respected and which assures Turkey’s active guarantorship.”

Although relations between the two communal leaders on the island are probably the best in the island’s history, that goodwill would have to be tested in a referendum. And no one in European politics knows more than Boris Johnson and Theresa May how unpredictable referendums can be.