From the perspective of human mobility, the COVID-19 pandemic constituted a natural experiment of enormous reach in space and time. Here, we analyse the inherent multiple scales of human mobility using Facebook Movement maps collected before and during the first UK lockdown. Firstly, we obtain the pre-lockdown UK mobility graph and employ multiscale community detection to extract, in an unsupervised manner, a set of robust partitions into flow communities at different levels of coarseness. The partitions so obtained capture intrinsic mobility scales with better coverage than nomenclature of territorial units for statistics (NUTS) regions, which suffer from mismatches between human mobility and administrative divisions. Furthermore, the flow communities in the fine-scale partition not only match well the UK travel to work areas but also capture mobility patterns beyond commuting to work. We also examine the evolution of mobility under lockdown and show that mobility first reverted towards fine-scale flow communities already found in the pre-lockdown data, and then expanded back towards coarser flow communities as restrictions were lifted. The improved coverage induced by lockdown is well captured by a linear decay shock model, which allows us to quantify regional differences in both the strength of the effect and the recovery time from the lockdown shock.