Significant nonresponse to the UK census presented major challenges to the estimation of the full population in both 1991 and 2001. In this paper I follow the implementation of agreed quality assurance strategies and their further development in response to the lack of confidence in the initial population estimates, but argue that the published census data are more accurate than in 1991. The strategy to complete the census database with records informed by the quality assurance procedures largely worked and should be maintained. Published census output and population estimates for England and Wales and for subnational areas contain significant uncertainty which is likely to remain for this and future decades. Both the estimates and the remaining uncertainty should be measured more precisely.