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(Abridged) We have used Gaia 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 carry out a non-parametric analysis of proper motions and membership determination. We investigate the reddening and proper motions of several dozen OB stars and red supergiants < 1 deg away from Wd 1. We identify a population of kinematic members of Wd 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. Extinction in this direction increases by a large amount around 2.8 kpc, due to dark clouds associated to the Scutum-Crux arm. As a consequence, we hardly see any stars at distances comparable to that of the cluster. The proper motions of Wd 1, however, are very similar to those of stars in the field surrounding it, but distinct. We find a second, astrometrically well-defined population in the foreground ($d\approx2\:$kpc), likely connected to the possible open cluster BH197. Wd 1 is very elongated, an effect not driven by the very heavy extinction to the East and South. We find a low-density halo extending up to 10' from the cluster centre, mainly in the NW quadrant. A few OB stars at larger distances from the cluster, most notably the LBV MN48, share its proper motions, suggesting that Wd 1 has little or no peculiar motion with respect to the field population of the Norma arm. However, 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. 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%.