Post-imperial Muslim migration to Europe followed former colonial ties

Evidence

Great numbers did, however, go and settle in Europe in the post-imperial years. Many of them went from former dependencies to the homelands of their former rulers—North Africans to France, south Asians to Britain, Indonesians to Holland, Trans-Caucasians and Central Asians to Russia. But these were not all. There were also many immigrants from countries that had never known imperial rule, notably economic migrants from Turkey and political and religious refugees from Iran. By now there are many millions of Muslim residents in most of the countries of Western Europe, an increasing proportion born and brought up in these countries, with all the expectations to which their birth entitles them and which their education prepares them to demand. — Bernard Lewis, From Babel to Dragomans, 705