When Rubar and Bestoon Abass embarked on their journey to Europe they had no idea that Cyprus was the continent’s easternmost state. Like most Iraqi Kurds heading west, their destination was Germany, not an EU nation barely 100 miles from war-torn Syria.

“I had never heard of Cyprus,” said Rubar, reaching for his pregnant wife’s hand as they sat gloomily in a migrant centre run by the Catholic charity Caritas in the heart of Nicosia. “The smugglers told us it was much cheaper to get to and was still in Europe. We paid $2,000 [£1,590] for the four of us to come.”

Cyprus is in the midst of a burgeoning migrant crisis as smuggler networks take advantage of the Mediterranean island’s partition and proximity to the Middle East. As in Greece, when Europe’s refugee crisis erupted with Syria’s descent into civil war, support groups have rushed to deal with the social ailments that have arisen with the influx.

“Cyprus is saturated,” its interior minister, Constantinos Petrides, said in an interview with the Guardian. “It’s no longer easy to absorb such flows, or handle the situation, no matter how much money we get.”

Facebook Twitter Pinterest A migrant from Iraq in his makeshift accommodation in Nicosia. Photograph: Petros Karadjias/AP

The island has exceeded every other EU member state in asylum claims in 2018, recording the highest number per capita with almost 6,000 applications for a population of about 1 million.

By August requests were 55% higher than for the same eight-month period in 2017, a figure itself 56% higher than that for 2016, according to the interior ministry. With the country’s asylum and reception systems vastly overstretched, alarmed officials have appealed to Brussels for help.

“This is a European problem,” said Petrides, adding that closed borders elsewhere in the bloc were placing a disproportionate burden on small frontline states such as Cyprus. “It’s absolutely necessary to find a holistic solution … which means distributing asylum seekers through an automatic relocation mechanism to countries throughout the EU.”

Rubar and Bestoon arrived with their two children in August. Like the ever-growing number of Syrians also heading here from overcrowded camps in Turkey and Lebanon, the couple landed in Northern Cyprus, the self-styled state acknowledged only by Ankara in the 44 years since Turkish troops invaded and seized over a third of the island’s territory.

They then took the increasingly well-trodden route of sneaking across the dividing buffer zone into the internationally recognised Greek-controlled south. Stretching 112 miles across Cyprus, the UN-patrolled ceasefire line offers innumerable blind spots for those determined to evade detection.

Geography’s stark reality hit, Rubar admits, when he was shown Cyprus on the world map adorning the migrant centre’s airy reception room. “If I had known I’d never have come,” said the farmer. “After all, being here we’re much nearer Baghdad than we are Berlin.”

Elizabeth Kassinis, Caritas’ executive manager, said the Abbasses’ experience is not uncommon. “Many are surprised to find out where they actually are. When we tell them, they are shocked, stunned, completely speechless. Nearly all arrive expecting they’ll be within walking distance of a job in Germany.”

Illicit crossings from the north have made Cyprus’ woes much worse. Reports have increased in recent months of irregular migrants flying into Ercan airport in the Turkish-controlled breakaway state.

Hamstrung by politics, not least Turkey’s refusal to recognise the government in the southern part of Cyprus since its 1974 invasion of the island, authorities are unable to send them back.

“Because of the illegal occupation in the north we’ve seen phenomena that wouldn’t happen in conditions of legality,” said Petrides. “It’s an open wound, not just for Cyprus but the entire EU.”

With international agencies focusing almost entirely on sea arrivals, the real number of migrants on the island has been hugely underestimated, charities say. “We are a humanitarian organisation that addresses poverty, hunger and homelessness and we are seeing across-the-board increases in them all,” Kassinis said.

A backlog of 8,000 asylum claims has amassed as authorities struggle to cope with the flows, according to the UN refugee agency, UNHCR. “We’re talking about a process that can take up to five years and an extremely high number of people waiting for final decisions to their claims,” said Katja Saha, the agency’s representative in Nicosia.

“It’s highly likely that the vast majority are not refugees and should not be in the asylum processing system but, that said, the lack of infrastructure and social services makes it very difficult to identify those who are vulnerable, particularly victims of trafficking and torture.”

As numbers grow, pressure on the island’s two state-run camps has become immense and asylum seekers are expected to find private accommodation after 72 hours. For most that is nearly impossible when rent allowances are little more than €100 (£90) per person a month and employment is limited to manual work such as car washing and farm labour, Saha said.

In Nicosia, which houses one of the camps, asylum seekers have resorted to sleeping in parks and buses and the vestibules of buildings. “For the last month I’ve been in a tent in the park with my wife and four children,” said Basin Hussain, who also fled Iraq. “The first three days were spent in the reception centre but then we were told to leave.”

Facebook Twitter Pinterest Basin Hussain with his asylum application in Nicosia. Photograph: Helena Smith/The Guardian

There are fears the drama being played out in the eastern Mediterranean will get a lot worse if the situation in Syria deteriorates further and war extends to Idlib, the country’s last rebel stronghold. A Turkish-Russian ceasefire deal is currently sustaining a fragile peace in the province.

Cyprus had been spared the refugee crisis until this year as most Europe-bound asylum seekers headed for Greece and Italy instead.

“It’s surprising, given its geographic location, that Cyprus has not been more impacted by the seven-year conflict,” said Saha. “Since the spring we’ve seen this increase in Syrians because word has spread that Lebanon and Turkey, as first asylum countries, are saturated.”

As elsewhere in Europe the island is not immune to hostility toward the new arrivals. Far-right groups coalescing around the ultranationalist ELAM party have gained increasing popularity as the issue provides fodder for their approval ratings ahead of European parliamentary elections next year.

“What we don’t want to do is open more and more reception centres,” said Petrides, emphasising that solidarity was now needed on Europe’s eastern edge. “It’s not the solution, either for the country or asylum seekers.”