European railways were ground zero Wednesday in faltering efforts to contain the continent’s burgeoning refugee crisis, with thousands of asylum-seekers camped out at Hungary’s main train station and service between Paris and London disrupted overnight after reports of migrants on the tracks.

A day after Hungary temporarily halted rail traffic at Budapest’s central station, at least 2,000 asylum seekers remained locked out, as Hungarian authorities refused to let them travel onward to Austria and Germany.

Several hundred staged impromptu demonstrations, shouting “Freedom! Freedom!” and demanding that they be allowed to use the tickets that many had already purchased for hundreds of euros. Riot police looked on warily as the protests continued into the evening.

Meanwhile, across the continent, passengers on the Eurostar service between Britain and France were stranded for hours overnight and two trains turned back as authorities searched for migrants who had been reported on the tracks and atop train carriages.

The delays disrupted travel for as many as 2,000 passengers and were the latest in a summer in which migrants have frequently ventured onto tracks near the Channel Tunnel in the French port city of Calais, trying to stow away on trains bound for Britain.

The impact on transit systems reflected the scale of the crisis confronting European leaders as hundreds of thousands of refugees have arrived seeking sanctuary from conflict, oppression and poverty in the Middle East, South Asia and Africa.

Policymakers have called an emergency summit for Sept. 14 at which European Union leaders are planning to push for a more coordinated effort by the union’s 28 member states.

The plans are expected to include a system for dispersing refugees more equitably across the continent, as well as rules for determining which migrants should be returned to their home countries because they fail to meet the definition of refugees.

But rights advocates say the E.U. also needs to implement safe and legal routes to the continent to allow refugees to avoid perilous and often deadly journeys.

The latest deaths were reported Wednesday when 12 migrants drowned after two boats capsized in the narrow strait between Turkey and the Greek island of Kos, Turkish police said.

The deaths highlighted the growing hazards of what had until recently been one of the safer routes to Europe because of the relatively brief sea journey.

A photo of a Syrian toddler whose body washed up on the Turkish coast hours after the sinkings circulated widely online. A second photo showed a solemn policeman cradling the boy, who was dressed in a red T-shirt, shorts and sneakers.

“Despite only being a few short miles, as we have seen, the open-sea journey from Turkey to Greece is far from safe and will only become more dangerous as the weather turns this autumn,” said Kirk Day, field director for the International Rescue Committee, in a statement. “With an estimated 200,000 refugees still planning to make the journey to Greece this year, it is inevitable that we will see a further loss of life until Europe’s policies change.”

The European border control agency Frontex said 23,000 migrants arrived in Greece last week alone — a 50 percent increase over the previous week. The total for the year in Greece is more than 200,000.

The vast majority of the migrants have no intention of staying in Greece but plan to travel north through the Balkans, Hungary and Austria to settle in northern European countries such as Germany and Sweden.

Germany has said it expects 800,000 asylum applications this year and has called for other countries to take up more of the burden.

But British Prime Minister David Cameron signaled Wednesday that his country would not necessarily comply. Britain has resettled just 216 Syrian refugees since the war began, in addition to nearly 5,000 others who have traveled to the island nation on their own.

Despite growing pressure from opposition politicians and fellow European leaders for those numbers to be expanded, Cameron said Wednesday that Britain would continue to focus on foreign aid rather than refugee resettlement.

“I don’t think there is an answer that can be achieved simply by taking more and more refugees,” he told the BBC.

Michael Birnbaum in Brussels contributed to this report.

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