Context. Recent observational studies indicate that a large number of OB stars are found within binary systems which may be expected to interact during their lifetimes. Significant mass transfer or indeed merger of both components is expected to modify evolutionary pathways, facilitating the production of exceptionally massive stars which will present as blue stragglers. Identification and characterisation of such objects is crucial if the efficiency of mass transfer is to be established; a critical parameter in determining the outcomes of binary evolutionary channels. Aims. The young and coeval massive cluster Westerlund 1 hosts a rich population of X-ray bright OB and Wolf–Rayet stars where the emission is attributed to shocks in the wind collision zones of massive binaries. Motivated by this, we instigated a study of the extremely X-ray luminous O supergiants Wd1-27 and -30a. Methods. We subjected a multi-wavelength and -epoch photometric and spectroscopic dataset to quantitative non-LTE model atmosphere and time-series analysis in order to determine fundamental stellar parameters and search for evidence of binarity. A detailed examination of the second Gaia data release was undertaken to establish cluster membership. Results. Both stars were found to be early/mid-O hypergiants with luminosities, temperatures and masses significantly in excess of other early stars within Wd1, hence qualifying as massive blue stragglers. The binary nature of Wd1-27 remains uncertain but the detection of radial velocity changes and the X-ray properties of Wd1-30a suggest that it is a binary with an orbital period ≤10 days. Analysis of Gaia proper motion and parallactic data indicates that both stars are cluster members; we also provide a membership list for Wd1 based on this analysis. Conclusions. The presence of hypergiants of spectral types O to M within Wd1 cannot be understood solely via single-star evolution. We suppose that the early-B and mid-O hypergiants formed via binary-induced mass-stripping of the primary and mass-transfer to the secondary, respectively. This implies that for a subset of objects massive star-formation may be regarded as a two-stage process, with binary-driven mass-transfer or merger yielding stars with masses significantly in excess of their initial “birth” mass.