Studies on migration and integration in Britain have noted the paucity of research on ‘new’ migrants, especially ‘illegal’ migrants and asylum seekers. This paper focuses on one understudied group - Albanian immigrants and their children - and looks at their migration and settlement, based on sixty interviews conducted in two phases either side of a 2003 mini-amnesty that gave many indefinite leave to remain. This regularization is the fulcrum around which our analytical narrative is built. Focusing on the interaction of migrants’ agency with host-country structure, the paper shows that an unsettled asylum policy and delays in implementation have had deleterious effects on migrants’ integration and sense of belonging, even after citizenship acquisition. As they search for a social and ethnic positioning within a multi-ethnic host society, the eventual realization of Albanians’ migration project is accompanied by culture shock, intergenerational difference and ambivalence towards integration.