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 red supergiants less than one degree away from Westerlund 1. Results. We identify a population of kinematic members of Westerlund 1 that largely includes the known spectroscopic members. From their EDR3 parallaxes, we derive a distance to the cluster of $ 4.23^{+0.23}_{-0.21} $ kpc. We analyse the extinction in this direction, finding that it increases by a large amount around 2.8 kpc, which in all likelihood is due to dark clouds associated with the Scutum-Crux arm. As a consequence, we hardly see any stars at distances comparable (or higher) than that of the cluster. The proper motions of Westerlund 1, however, are very similar to those of stars in the field surrounding it which are – almost without exception – less distant, but distinct. We find a second, astrometrically well-defined population in the foreground (d ≈ 2 kpc), centred ∼8′ away, which is likely connected to the possible open cluster BH 197. Westerlund 1 is very elongated, an effect that seems real and not driven by the very heavy extinction to the east and south. We find a low-density halo extending to distances up to 10′ from the cluster centre, mainly in the north-west quadrant. A few OB stars at larger distances from the cluster, most notably the luminous blue variable (LBV) MN48, share its proper motions, suggesting that Westerlund 1 has little or no peculiar motion with respect to the field population of the Norma arm. Despite this, we are unable to find any red supergiant that could belong to an extended population related to the cluster, although we observe several dozen such objects in the foreground, demonstrating the richness of the field population along this sightline. We find a substantial population of luminous OB members obscured by several more magnitudes of extinction than most known members. These objects, mostly located in the central region of the cluster, increase the population of OB supergiants by about 25%.