Context. Gaia DR3 has offered the scientific community a remarkable dataset of approximately one million spectra acquired with the radial velocity spectrometer (RVS) in the calcium II triplet region, which is well suited to identify very metal-poor (VMP) stars. However, over 40% of these spectra have no released parameters by Gaia's GSP-Spec pipeline in the domain of VMP stars, whereas VMP stars are key tracers of early Galactic evolution.|Aims. We aim to provide spectroscopic metallicities for VMP stars using Gaia RVS spectra, thereby producing a catalogue of bright VMP stars distributed over the full sky that can serve as the basis for studies of early chemical evolution throughout the Galaxy.|Methods. We selected VMP stars using photometric metallicities from the literature and analysed the Gaia RVS spectra to infer spectroscopic metallicities for these stars.|Results. The inferred metallicities agree very well with literature high-resolution metallicities, with a median systematic offset of 0.1 dex and standard deviation of similar to 0.15 dex. The purity of this sample in the VMP regime is similar to 80%, with outliers representing a mere similar to 3%.|Conclusions. We have built an all-sky catalogue of similar to 1500 stars available, featuring reliable spectroscopic metallicities down to [Fe/H] similar to -4.0, of which similar to 1000 are VMP stars. More than 75% of these stars have either no spectroscopic metallicity value in the literature to date or have been flagged as unreliable in their literature spectroscopic metallicity estimates. This catalogue of bright (G < 13) VMP stars is three times larger than the current sample of well-studied VMP stars in the literature in this magnitude range, making it ideal for high-resolution spectroscopic follow-ups and studies of the properties of VMP stars in different parts of our Galaxy.