Aims:Based on a new set of sulphur abundances in very metal-poor stars and an improved analysis of previous data, we aim at resolving current discrepancies on the trend of S/Fe vs. Fe/H and thereby gain better insight into the nucleosynthesis of sulphur. The trends of Zn/Fe and S/Zn will also be studied. Methods: High resolution VLT/UVES spectra of 40 main-sequence stars with -3.3 < [Fe/H] < -1.0 are used to derive S abundances from the weak λ 8694.6 S I line and the stronger λ λ 9212.9,9237.5 pair of S I lines. For one star, the S abundance is also derived from the S I triplet at 1.046 μm recently observed with the VLT infrared echelle spectrograph CRIRES. Fe and Zn abundances are derived from lines in the blue part of the UVES spectra, and effective temperatures are obtained from the profile of the Hβ line. Results: Comparison of sulphur abundances from the weak and strong S I lines provides important constraints on non-LTE effects. The high sulphur abundances reported by others for some metal-poor stars are not confirmed; instead, when taking non-LTE corrections into account, the Galactic halo stars distribute around a plateau at [S/Fe] ~ +0.2 dex with a scatter of 0.07 dex only. [Zn/Fe] is close to zero for metallicities in the range -2.0 < [Fe/H] < -1.0 but increases to a level of [Zn/Fe] ~ +0.1 to +0.2 dex in the range -2.7 < [Fe/H] < -2.0. At still lower metallicities [Zn/Fe] rises steeply to a value of [Zn/Fe] ~ +0.5 dex at [Fe/H] = -3.2. Conclusions: The trend of S/Fe vs. Fe/H corresponds to the trends of Mg/Fe, Si/Fe, and Ca/Fe and indicates that sulphur in Galactic halo stars has been made by α-capture processes in massive SNe. The observed scatter in S/Fe is much smaller than predicted from current stochastic models of the chemical evolution of the early Galaxy, suggesting that either the models or the calculated yields of massive SNe should be revised. We also examine the behaviour of S/Zn and find that departures from the solar ratio are significantly reduced at all metallicities if non-LTE corrections to the abundances of these two elements are adopted. This effect, if confirmed, would reduce the usefulness of the S/Zn ratio as a diagnostic of past star-formation activity, but would bring closer together the values measured in damped Lyman-alpha systems and in Galactic stars. Based on observations collected at the European Southern Observatory at Paranal, Chile (programmes No. 67.D-0106, 73.D-0024 and CRIRES science verification program 60.A-9072). Table 1 and Appendices are only available in electronic form at http://www.aanda.org