Estimates of migration from a national census are essential ingredients of population analysis for subnational areas. The impact of incomplete data became an issue in Britain, because evidence after its 1991 Census suggested that the 2% undercount was concentrated in particular demographic and social groups. A review of the social dimensions of non-response in past censuses, together with the official estimates of non-response for demographic categories, have been used to estimate a range for the number missing from each census flow of migrants between local authority districts in Britain. In total around 23% is added to the published count of migrants. The impact of the missing migrants is shown to have overestimated the scale of counterurbanisation, but not to account for the entire phenomenon. Non-response, when included in estimates of migration, does eliminate entirely the excess of females among young adult migrants observed in the 1991 census. In official population projections, the main effect of including an allowance for non-respondents is to reduce considerably the net flows out of city districts. Measures to include estimates of non-response within the published census counts are necessary. Plans for a ‘One number census’ in 2001 may much reduce the biases within the UK census counts of migrants. Copyright © 1999 John Wiley & Sons, Ltd.