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Westerlund 1 (Wd 1) is one of the most relevant star clusters in the Milky Way to study massive star formation, although it is still poorly known. Here, we used photometric and spectroscopic data to model the eclipsing binary W36, showing that its spectral type is O6.5 III  +  O9.5 IV, hotter and more luminous than thought before. Its distance d W36 = 4.03 ± 0.25 kpc agrees, within the errors, with three recent Gaia-EDR3-based distances reported in Paper I, Beasor & Davies, and by Negueruela's group. However, they follow different approaches to fix the zero-points for red sources such as those in Wd 1, and to select the best approach, we used an accurate modelling of W36. The weighted mean distance of our parallax (Paper I) and binary distances results in d wd1 = 4.05 ± 0.20 kpc, with an unprecedented accuracy of 5 per cent. We adopted isochrones based on the Geneva code with supersolar abundances to infer the age of W36B as 6.4 ± 0.7 Myr. This object seems to be part of the prolific star formation burst represented by OB giants and supergiants that occurred at 7.1 ± 0.5 Myr ago, which coincides with the recently published PMS isochrone with age 7.2 Myr. Other BA-type luminous evolved stars and yellow hypergiants spread in the age range of 8–11 Myr. The four red supergiants discussed in paper I represent the oldest population of the cluster with an age of 10.7 ± 1 Myr. The multiple episodes of star formation in Wd 1 are reminiscent of that reported for the R136/30 Dor LMC cluster. [ABSTRACT FROM AUTHOR]