Context. BA-type supergiants are amongst the most optically-bright stars. They are observable in extragalactic environments, hence potential accurate distance indicators. Aims. An extensive record of emission activity in the Hα line of the BA supergiants β Orionis (Rigel, B8Ia) and α Cygni (Deneb, A2Ia) is indicative of localized time-dependent mass ejections. However, little is known about the spatial distribution of these apparent structures. Here, we employ optical interferometry to study the Hα line-formation region in these stellar environments. Methods. High spatial- (~0.001$\arcsec$) and spectral- (R = 30 000) resolution observations of Hα were obtained with the visible recombiner VEGA installed on the CHARA in...