BRUSSELS — The city is freezing. At night, Hamza Khater eats and sleeps at a volunteer-run shelter. He spends his days hanging around the international bus stop next to the Gare du Nord.

“What am I looking for? I am looking for a life,” said Mr. Khater, 31, who fled the violence-ravaged Sudanese region of Darfur a year ago. Specifically, he is looking for a chance to reach Britain. He has been for months.

Sudanese migrants like Mr. Khater are increasingly visible in Brussels, around train stations, in public squares and parks, sometimes sleeping in the streets. Mehdi Kassou, an organizer for a volunteer group that provides shelter for about 500 migrants each night, estimates that about 45 percent of them are Sudanese.

Their presence reflects the latest phase in a migration crisis that has disrupted politics in one European country after another. It also leaves the center-right government of Belgium, which is set to hold elections next year, struggling to reconcile its legal and humanitarian obligations with its “tough but fair” rhetoric on migration, and a determination to avoid large-scale migrant camps in the capital.