Even before it became a holding pen, Moria was a pretty poor registration centre, unable to provide basic facilities and painfully slow to process the thousands of refugees and migrants who arrive on the shores of Lesbos every week.

But since midnight on Sunday, when the new EU-Turkey migrant deal came into force, refugees have been picked up by the coastguard and transported directly to Moria by the Greek authorities.

The camp has become an open-air prison, a compound of temporary buildings on a hill overlooking the coast of this island, not far from Turkey’s Mediterranean coast. It is to here that all arrivals must wait for the news their long struggle to reach Europe will almost certainly get them no further than the Greek islands.

They will be returned to Turkey, which the European Union has now declared a safe country, in its bid to stem the biggest refugee crisis since the Second World War.

The lightning fast implementation of the deal, signed last Friday, has stretched to the limit the capacity of the Greek government, which has no means to process the asylum claims that everyone who arrives has the right to make. Those who came looking for peace and a better life have instead found themselves locked up, and handed detention papers. In response, aid agencies have dropped out of their involvement at the centre one by one, refusing to be associated with the detention of migrants – among whom are more than 100 unaccompanied children. Oxfam this week said the development was “an offence” to Europe’s values.

“They have told us nothing,” says Naima Abdullah, 28, speaking through the chain link fence, her four-year-old daughter Mirna by her side. She paid $2,000 for herself, Mirna, and her one-month-old baby to cross the sea from Turkey after fleeing air strikes in rural Damascus three months ago. She arrived on Sunday, in the first boats after the deal came into force. But four days later, she still hadn’t been given an opportunity to register a claim for asylum.

And as the numbers grow, observers worry the only possible outcome will be the mass expulsions Europe has promised to avoid. Nadine Abuasil, 25, said she came to Lesbos because life in Turkey since she fled Deraa in Syria a month ago was not worth living. Her family were blackmailed for money by local gangs, and there was no work in a country that is expensive to live in. “We cannot go back to Turkey,” she says simply. She and her 23-year-old brother arrived on Sunday after a five hour boat journey during which two men died. They had apparently suffocated.

She points to the ground of the detention centre. “We would rather die here than in Turkey.” Her brother, Mohammed, was no less emphatic when asked what he’d do if he was forced to return. “I don’t speak English,” he says. “But: kill myself, kill myself.”

The deal has been decried by human rights groups and legal experts who question if Turkey can be considered a safe third country for the forcible return of migrants, and if Greece, which has floundered under the pressure of more than one million refugees arrivals in the past year, is capable of processing asylum claims – even with promised outside help.

“Greece has effectively been asked to build an asylum system in two weeks,” says Camino Mortera, a research fellow for the Centre for European Reform and a specialist in EU law. “The EU claims there won’t be returns en masse but if you are not able to process people in a regulated fashion, how else are they going to deal with this?”

As a detention centre Moria is barely adequate, including to the task of holding people in – a handful jump the fence at ease and unnoticed, disappearing into the woodland. They have nowhere to go once they’re out and often come back. People have been forced to sleep on the chalky gravel, wrapped in blankets. Among them are a frail elderly man, and Elham, 14, from Afghanistan who fled along with her family from threats from the Taliban.

“We asked the police for information, they just say ‘We don’t know’,” said Elham. Tensions are simmering, with accusations some nationalities are receiving preferential treatment over others.

Naima Abdullah, with her two small children, wants to reach Germany, where her husband is now claiming asylum. It’s not clear what will happen to the many families that have been separated this way. Much about the deal is unclear, even to the Greek authorities. “It’s not clear how long people will stay,” said UNHCR spokesperson Boris Cheshirkov . “It’s still not clear how the deal will be implemented, how Greece will be given capability to deal with asylum claims.”

Tove Ernst, a spokesperson for migration at the European Commission said the intention was to have people moved from the facilities swiftly, adding: “Detention in cases of returns should always be limited.”

Frontex border agency this week called on EU member states to step up and provide extra personnel to help authorities on Lesbos manage the new deal. So far, only 396 of 1,500 requested police officers have been offered. There are plans to send an extra 50 immigration experts, with five arriving from Turkey this week.

Marios Andriotis, a senior adviser to the Lesbos mayor, is visibly strained. He said the local government was doing its best to provide for new arrivals. But, he added: “We are a small municipality and we do not decide the union’s policies. We are looking for a contingency plan, a waiting area where we could accommodate 5,000 to 10,000 people.” The deal’s success relies on people like Ms Abdullah deciding to wait their turn under the one-for-one scheme, under which Europe has agreed to take a Syrian refugee directly from Turkey, in exchange for each Syrian Turkey accepts back from Greece.

The numbers have shown some signs of slowing. Coast guards heading out for a patrol on Thursday said they didn’t expect to pick up anyone.

Fadi, 23, who declined to give his family name, arrived in Lesbos after fleeing army conscription in Syria. He escaped to Turkey at the end of last year, paying bribes along the way to the regime and to Isis. When he left Turkey, he had no idea an effective prison would be awaiting him in Greece.

He says he wouldn’t have come if he had known. “They treat us like animals here,” he said, shouting across a ditch that runs along one side of Moria’s chainlink fence. “I feel like I am in Syria.” Still, he doesn’t think the deal will contain the refugees for long. “People are fleeing a war. They will find a way,” he said

In any case, Europe agreed to take only 72,000 Syrians under the plan; more than twice that number arrived in Greece last October alone. And there is doubt that member states will hold up their end of the bargain in taking in refugees; previous attempts to impose a quota system to share the burden have swiftly fallen apart.

Europe hopes, too, many can be persuaded to stay in Turkey. It has promised an extra €3bn to Ankara to help provide aid to its 2.7 million Syrian refugees. But with little work and education for Syrians in Turkey, many are on the point of destitution and may take some convincing that they have a future there.

If people come anyway, the Greek islands will be swiftly overwhelmed. Their combined facilities have a capacity of just 7,490, already more than half full. And in the first five days since the deal came into effect, more than 1,400 had made the journey to the islands.