Context. Abundances of beryllium in metal-poor stars scale linearly with metallicity down to [Fe/H] ∼ −3.0. In the stars where Be has been detected at this extremely metal-poor regime, an increased abundance scatter has been previously reported in the literature. This scatter could indicate a flattening of the relation between Be abundances and metallicity. Aims. Our aim is to perform a new investigation of Be abundances in extremely metal-poor stars and try to clarify whether a Be abundance plateau exists. We revisited the Be abundances in a sample of nine dwarfs with metallicities close to [Fe/H] ∼ −3.0. Additionally, we analysed the Be lines in the spectra of stars BPS BS 16968-0061 and CD-33 1173 for the first time. Methods. We took advantage of Gaia DR2 parallaxes to refine values of the surface gravity of the stars. Updated values of surface gravity can have a significant impact on the determination of Be abundances. The other atmospheric parameters were computed using photometric and spectroscopic data. Abundances of Be were determined using spectrum synthesis and model atmospheres.Results. Some of the stars indeed suggest a flattening. Over about a 0.5 dex range in metallicity, between [Fe/H] ∼ −2.70 and −3.26, the Be abundances stay mostly constant at about log(Be/H) ∼ −13.2 dex. Nevertheless, for several stars, we could only place upper limits that are below that level. Most of the sample stars are consistent with having been formed at the progenitor of the so-called Gaia-Enceladus merger. Two out of the three stars likely formed in-situ are the ones that deviate the most from the linear relation. Conclusions. The mixed origin of these extremely metal-poor stars offers a clue to understanding the flattening. We suggest that our observations can be naturally understood as a consequence of the inhomogeneous star forming conditions in the early Galaxy. Without efficient mixing, the early interstellar medium would be characterised by a large scatter in Fe abundances at a given moment. Beryllium, on the other hand, because of its origins in cosmic-ray spallation, would have more homogeneous abundances (in a Galaxywide sense). We therefore suggest that the observed flattening of the Be-versus-metallicity relation reflects a stronger scatter in the Galactic Fe abundances at a given age.