We have observed the B I 2497 A line to derive the boron abundances of two very metal-poor stars selected to help in tracing the origin and evolution of this element in the early Galaxy: BD +23 3130 and HD 84937. The observations were conducted using the Goddard High Resolution Spectrograph on board the Hubble Space Telescope. A very detailed abundance analysis via spectral synthesis has been carried out for these two stars, as well as for two other metal-poor objects with published spectra, using both Kurucz and OSMARCS model photospheres, and taking into account consistently the NLTE effects on the line formation. We have also re-assessed all published boron abundances of old disk and halo unevolved stars. Our analysis shows that the combination of high effective temperature (Teff > 6000 K, for which boron is mainly ionized) and low metallicity ([Fe/H]<-1) makes it difficult to obtain accurate estimates of boron abundances from the B I 2497 A line. This is the case of HD 84937 and three other published objects (including two stars with [Fe/H] ~ -3), for which only upper limits can be established. BD +23 3130, with [Fe/H] ~ -2.9 and logN(B)_NLTE=0.05+/-0.30, appears then as the most metal-poor star for which a firm measurement of the boron abundance presently exists. The evolution of the boron abundance with metallicity that emerges from the seven remaining stars with Teff < 6000 K and [Fe/H]<-1, for which beryllium abundances were derived using the same stellar parameters, shows a linear increase with a slope ~ 1. Furthermore, the B/Be ratio found is constant at a value ~ 20 for stars in the range -3<[Fe/H]<-1. These results point to spallation reactions of ambient protons and alpha particles with energetic particles enriched in CNO as the origin of boron and beryllium in halo stars.