Mobility data have demonstrated major changes in human movement patterns in response to COVID-19 and associated interventions in many countries. This can involve sub-national redistribution, short-term relocations as well as international migration. In this paper, we combine detailed location data from Facebook measuring the location of approximately 6 million daily active Facebook users in 5km2 tiles in the UK with census-derived population estimates to measure population mobility and redistribution. We provide time-varying population estimates and assess spatial population changes with respect to population density and four key reference dates in 2020 (First lockdown, End of term, Beginning of term, Christmas). We also show how population estimates derived from the distribution of Facebook users vary compared to mid-2020 small area population estimates by the UK national statistics agencies. We estimate that between March 2020 and March 2021, the total population of the UK declined and we identify important spatial variations in this population change, showing that low-density areas have experienced lower population decreases than urban areas. We estimate that, for the top 10% highest population tiles, the population has decreased by 6.6%. Further, we provide evidence that geographic redistributions of population within the UK coincide with dates of non-pharmaceutical interventions including lockdowns and movement restrictions, as well as seasonal patterns of migration around holiday dates. The methods used in this study reveal significant changes in population distribution at high spatial and temporal resolutions that have not previously been quantified by available demographic surveys in the UK. We found early indicators of potential longer-term changes in the population distribution of the UK although it is not clear if these changes may persist after the COVID-19 pandemic.