Sometimes en masse, sometimes alone they keep on arriving: in rickety boats carrying men, women and children looking for a freedom they hope Europe will offer.

Despite winter’s limited daylight and whiplash-heavy storms and rains, the number of asylum seekers landing on Greek shores shows no sign of abating. Not since Europe’s historic agreement with Turkey to curb migrant flows at the height of Syria’s civil war in March 2016 have arrivals been so high.

In September alone 10,551 newcomers arrived, the highest in a single month since the deal.

The renewed surge has placed mounting pressure on a centre-right government that pledged to take a much tougher stance on migration than its predecessor. Since assuming office in July, prime minister Kyriakos Mitsotakis has appealed to the EU to exhibit more solidarity towards Greece and other frontline states struggling to cope with ever more refugees and migrants.

Latest figures show there are about 40,000 men, women and children on Samos, Lesbos, Chios, Kos and Leros – the five main entry points facing Turkey – mainly accommodated in overcrowded camps designed for 5,400. Despite concerted efforts to decongest the islands, the authorities have only been able to move about 10,000 people to the mainland in recent months.

The EU’s new executive body is poised to draft fresh policies on the migration challenge and Athens says it’s crucial that Brussels recognises the need for asylum seekers to be shared equally among member states.

Last week, Mitsotakis told the European Commission’s new vice-president, Margaritis Schinas, and home affairs commissioner Ylva Johansson – both tasked with overhauling migration and asylum policies – that Greece had “reached its limits” and could no longer handle the influx alone.

“This is not a Greek-Turkish problem,” he said as the officials visited Athens. “[It’s] an issue that affects the European Union as a whole and we are looking forward to your help, as well as a firm European policy, to address it.”

Targeted by people smugglers, Greece has been at the sharp end of migration flows, hosting close to 90,000 refugees and migrants nationwide – a greater number than the combined total of asylum seekers registered in Italy, Spain, Malta and Cyprus, according to the UNHCR.

Amid growing concerns over the appalling conditions, Brussels has come under pressure to take action. On 12 December, France said it would take in 400 people from Greece, but it is seen as too little, too late. At a time when the EU faces stiff resistance from within its own borders – not least from Visegrád countries led by Hungary – goodwill gestures will do little to distribute the load fairly, Greek officials say.

Late last month, the UN high commissioner for refugees, Filippo Grandi, also called for Europe to do more at a time of growing global displacement due to persecution and war.

Using a symbolic trip to Greece, he noted it was clear the compassion with which the nation had greeted over a million Syrians at the height of the crisis was now much “less visible ” – and at risk of running out.

“Europe has to get its act together,” he said after visiting Lesbos. “[It] has to have a new system that is based on sharing, responsibility sharing.”

Regulations drafted 20 years earlier that required asylum seekers to register in first-entry countries were “completely inadequate now,” he said.

Even more worrying was the sheer number of unaccompanied minors arriving, who were most at risk of labour exploitation, sexual exploitation and violence, Grandi warned.

“There are more than 5,000 [in Greece] … there is a children on-the-move emergency in this country that needs to be tackled.”

Elected on a tough law and order platform, the Mitsotakis government has announced measures aimed squarely at deterrence and deportation of those not entitled to remain in Europe.

Among the policies is a controversial plan to replace the sprawling island camps with “closed” detention centres, which human rights groups claim will be tantamount to “prisons”.

The new administration has also announced plans to accelerate asylum procedures while relocating up to 20,000 to the mainland from islands.

As anti-immigrant rhetoric mounts across the continent, the UN has voiced fears over the prospect of harsh measures being applied to people desperately in need of protection, access to education and health services.

“I made it clear to the [Greek] government that UNHCR policy is against detaining asylum seekers … seeking asylum is not a crime,” Grandi insisted, distinguishing between the Greek government’s right to control the process of managing refugees and it pursuing detainment.

“We are all in favour of efficiency and speed, but not if this is at the expense of safeguards,” he said.

Greece is not alone in recording a jump in arrivals this year. Cyprus has experienced a surge, with most refugees travelling into the partitioned island’s Greek south through the Turkish-occupied north.

Cyprus outstrips all other EU states in having the highest number of asylum applications per capita.

“At present rates, Cyprus will have 100,000 [refugees and economic migrants] in the next five years,” said Constantinos Petrides, the country’s interior minister until this month.

“And, frankly, that estimate is rather modest,” he told the Guardian. “It’s a lot of people for a country the size of Cyprus.”

His successor announced this week that Greek Cypriot police and military would be stepping up patrols along the island’s UN-patrolled ceasefire line.

Meanwhile Turkish president Recep Tayyip Erdoğan repeatedly threatens “to open the gates” for refugees to Europe. Attitudes in Turkey, where almost four million Syrians are registered, have hardened dramatically this year on the back of economic crisis and spiralling joblessness.

With frontline states increasingly viewing the issue of migration as the EU’s single biggest policy failure, Greece, Cyprus and Bulgaria have formed the Eastern Mediterranean Migration Route Initiative – an alliance that has has also forged ties with Malta and Italy.

In a time of record population displacement, and with the bloc riven with division over how to handle the issue, the EU’s new executive promises to devise a common strategy to confront a phenomenon that shows no signs of slowing any time soon.