The ONS produces population estimates for England and Wales and local authorities within that area. Similar figures are produced for Scotland by National Records of Scotland, and for Northern Ireland by the Northern Ireland Statistics and Research Agency.
These estimates are derived by taking the population measured in the most recent census; ageing this on; then adjusting for births, deaths, international migration and internal migration (that is, migration within the UK).
A detailed explanation of the methods used for areas in England and Wales is provided in the Methods Guide for the National and Local Authority Population Estimates. (494.2 Kb Pdf)
Though broadly similar methods are adopted for population estimates for Scotland and Northern Ireland there are some differences in the detail. More information on this is available in the Comparison of data sources and methods document. (157.3 Kb Pdf)