Context. The young massive cluster Westerlund 1 offers the promise of a grand laboratory for the study of high-mass star evolution, but its basic parameters are still poorly known. Aims. In this paper, we aim at a better characterisation of the cluster by determining some basic kinematic properties and analysing the area surrounding the cluster and the population in its foreground. Methods. We have used Gaia early data release 3 (EDR3) data, together with spectra of a large sample of luminous stars in the field surrounding Westerlund 1, to explore the extent of the cluster. We carried out a non-parametric analysis of proper motions and membership determination. We investigated the reddening and proper motions of several dozen OB stars and r...