How well do immigrants entering the UK assimilate into recipient labour markets? Using the underexploited, sizeable and long Lifetime Labour Market Database between 1981 and 2006, we investigate the evolution of the immigrant-native earnings gap-a measure of immigrants' assimilation-across the entire earnings distribution, across cohorts and across nationalities. We are able to control for observable and unobservable individual-specific characteristics as well as for specific characteristics of both time periods and recipient labour markets, defined as small geographical areas, and crucially, for the interaction of the two, in a robust empirical model specification anchored in the human capital theory. We also control for cohort-specific effects and nationality-specific effects. Our results show little evidence of large or persistent earnings disparities across the earnings distribution, across cohorts or across nationalities. These findings are supportive evidence of successful assimilation of immigrants into the UK, suggesting that recipient labour markets primarily reward individuals' characteristics other than, and regardless of, their immigration status. Nevertheless, some distinctive features emerge. When investigating the evolution of the immigrant-native earnings gap over time, our results illustrate how immigrants from different continents and cohorts have very different assimilation trajectories.