British Prime Minister David Cameron has come under renewed pressure to accept refugees stranded in the so-called "jungle" camp in Calais, the French city just across the sea from Britain.
For the moment, Mr Cameron is rejecting this option. "I think it would be a very bad move to make Calais a magnet for even more people to come," he told Parliament in London on Monday.
But Labour opposition leader Jeremy Corbyn, who recently visited the Calais refugee camps, has renewed his appeals for Britain and France to "be a bit more human" about the humanitarian crisis confronting both nations.
And in another indication that the problem cannot be ignored, unrest among Calais refugees is increasing, with the city's port forced to close for hours over the weekend after asylum seekers forced their way on to a UK-bound ferry.
On any given day, hundreds of asylum seekers converge on Calais, the nearest spot between the two nations, trying to get onto trains or lorries which use the tunnel underneath the English Channel dividing Britain from the continent.
France and Britain have often blamed each other for this problem. The British have accused the French of tolerating the mayhem in the hope of getting rid of the migrants; under European rules, asylum seekers already in France are the responsibility of the French government, and are not entitled to choose to move to Britain.
The French retort that Britain is largely to blame for the situation: Mrs Natacha Bouchart, the outspoken Mayor of Calais, claims that illegal migrants perceive Britain as a "soft touch" for welfare benefits, and a better place to find jobs in the black economy than in France.
Despite these tensions, the immigration services on both sides collaborate closely. A Franco-British command centre to tackle the human-smuggling criminal networks was set up last year. Britain is expanding what it gingerly refers to as a "National Barrier Asset", essentially a fence on French territory near the entry point to the tunnel. Cameras and infra-red detectors scan lorries and trains entering the UK.
But the numbers of would-be asylum seekers still overwhelm existing safeguards. The UK Border Force and the French authorities together prevented more than 39,000 attempts to cross the Channel illegally in 2014/15, the last period for which accurate data is available. Many of those who fail to make it remain in Calais, hoping to get lucky later; the camps they occupy are referred to as "the jungle".
Mr Corbyn's decision to visit the camps and champion the cause of these migrants by calling on Britain to accept them has surprised political observers. A radical left-winger who took over the Labour leadership last September, Mr Corbyn is languishing in opinion polls, and arguing for the admission of foreigners is hardly a vote-winner: Labour lost the past two general elections in part because it was perceived to be soft on immigration.
Mr Cameron immediately pounced on Mr Corbyn's argument that by admitting "not more than 9,000" asylum seekers now in the Calais camps, Britain would resolve the migrants' problem. As Mr Cameron pointed out, far from clearing the camps, such a move would only invite even greater numbers.
Still, Mr Corbyn's decision to raise the matter may not be as outlandish as it seems. For although all opinion polls indicate that a majority of the public is against further immigration, Britons are also uneasy about appearing to be heartless.
In a parliamentary debate on Monday, Mr Cameron faced calls from some of his own MPs to make an exception and admit into the UK unaccompanied refugee children now languishing in camps. Mr Eric Pickles, a former senior Cabinet minister, drew parallels between the plight of such minors and a British initiative on the eve of World War II that saved almost 10,000 East European Jewish children from extermination by the Nazis. That is now considered as one of the most moving stories of the war. An imposing monument to the children, who arrived with just one suitcase each and a tag around their necks bearing their names, stands outside Liverpool Railway Station in the British capital.
For now, the British remain non-committal; all that Immigration Minister James Brokenshire is prepared to say is that the government's policy on child refugees remains "under review".
But both the British and the French governments know that ignoring the "jungles" being created in Calais is not a long-term answer.