In Hungary, hundreds of migrants yesterday protested for a second day in front of Budapest’s Keleti Railway Terminus, after they were blocked by police from boarding trains bound for Germany.

More than 2,000 migrants, including families with children, were waiting in the square at the station while Hungarians with IDs and foreigners with valid passports could get on the trains.

Germany, which is prepared to take by far the greatest number of refugees, has begun accepting asylum claims from Syrians regardless of where they entered the EU, even though undocumented migrants are barred from travel across the bloc. That has caused confusion for neighbouring countries, which have alternated between letting migrants through and halting them.

Italy announced new measures to add checks at its northern border in response to a German request.

In Hungary, the main arrival point for those crossing the Balkans by land, a government spokesman said the country would observe EU rules which bar travel by those without valid documents.

I don’t think there is an answer that can be achieved simply by taking more and more refugees

“I want my freedom, I have been on the road for a very long time, and now I am in the European Union, and I want my freedom,” said Sanil Khan, 32, leader of a group of about 100 young men who marched behind a cardboard Afghan flag near a crowd at the station. The perils of the voyage were brought home by the images of a toddler in red t-shirt, blue shorts and tiny sneakers, washed up on the beach in Turkey.

The migration crisis has confounded the EU, which is committed to the principle of accepting refugees fleeing real danger but has no mechanism to compel its 28 member states to share out the burden. Opinion across Europe has been increasingly polarised: German soccer fans have unveiled “refugees welcome” banners at matches, while a popular British newspaper columnist called migrants “cockroaches”.

Countries like Italy, Greece and Hungary say they need more help from EU partners.

Germany has been the most welcoming, with plans to accept hundreds of thousands of refugees this year alone, adding €3.3 billion to its welfare bill next year. A record 104,460 asylum seekers arrived in Germany last month.

But that has caused chaos for neighbours and threatened the Schengen system that abolished frontier checks among 26 European countries. Berlin says that despite its decision to accept asylum applications from Syrians who arrive elsewhere in the EU, other EU states must still demand migrants remain in the countries where they first register. At the opposite end of the spectrum of openness is Britain, which so far has accepted just 216 Syrian refugees under a scheme in partnership with the UN, as well as around 5,000 that managed to reach Britain and apply on their own.

“We have taken a number of genuine asylum seekers from Syrian refugee camps, and we keep that under review, but we think the most important thing is to try to bring peace and stability to that part of the world,” Prime Minister David Cameron said. “I don’t think there is an answer that can be achieved simply by taking more and more refugees.”