Refugees are often perceived as an economic ‘burden’, as the current debate on the European refugee crisis illustrates. But there is little quantitative evidence on the medium-term outcomes of refugees in the UK. We fill this gap by looking at the case of ‘East African Asians’ who arrived as refugees in the late 1960s and early 1970s. We discuss from a theoretical and empirical perspective the possible factors that might influence—positively and negatively—their long-term economic outcomes and use data from the UK Census to describe those outcomes 40 years later. We show that their outcomes are at least as good as the population average, with the younger cohort performing better, and better than for economic migrants of the same ethnicity. At least for this group, refugee status, as distinct from ethnicity or immigrant status, appears to have been positively associated with their economic outcomes.