The policies implemented to hinder the COVID-19 outbreak represent one of the largest critical events in history. The understanding of this process is fundamental for crafting and tailoring post-disaster relief. In this work we perform a massive data analysis, through geolocalized data from 13M Facebook users, on how such a stress affected mobility patterns in France, Italy and UK. We find that the general reduction of the overall efficiency in the network of movements is accompanied by geographical fragmentation with a massive reduction of long-range connections. The impact, however, differs among nations according to their initial mobility structure. Indeed, we find that the mobility network after the lockdown is more concentrated in the case of France and UK and more distributed in Italy. Such a process can be approximated through percolation to quantify the substantial impact of the lockdown.