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Abundances of beryllium in metal-poor stars scale linearly with metallicitydown to [Fe/H] ~ -3.0. In the stars where Be has been detected at thisextremely metal-poor regime, an increased abundance scatter has been previouslyreported. This scatter could indicate a flattening of the relation between Beand [Fe/H]. Our aim is to perform a new investigation of Be abundances inextremely metal-poor stars and try to clarify whether a Be abundance plateauexists. We revisited the Be abundances in a sample of nine dwarfs with [Fe/H] ~-3.0. Additionally, we analysed the Be lines in the spectra of stars BPS BS16968-0061 and CD-33 1173 for the first time. We took advantage of Gaia DR2parallaxes to refine values of the surface gravity of the stars. Abundances ofBe were determined using spectrum synthesis. Some of the stars indeed suggest aflattening. Between [Fe/H] ~ -2.70 and -3.26, the Be abundances stay mostlyconstant at log(Be/H) ~ -13.2 dex. Nevertheless, for several stars we couldonly place upper limits that are below that level. Most of the sample stars areconsistent with having been formed at the progenitor of the so-calledGaia-Enceladus merger. Two out of the three stars likely formed in-situ are theones that deviate the most from the linear relation. The mixed origin of thesestars offers a clue to understanding the flattening. We suggest that ourobservations can be understood as a consequence of the inhomogeneous starforming conditions in the early Galaxy. Without efficient mixing, the early ISMwould 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 Galaxy-wide sense). We thereforesuggest that the observed flattening of the Be-versus-Fe relation reflects astronger scatter in the Galactic Fe abundances at a given age [abridged].

Inhomogeneity in the early Galactic chemical enrichment exposed by beryllium abundances in extremely metal-poor stars