We have obtained high-resolution high signal-to-noise ratio spectra of the S I near-infrared doublet at 8694 Å in eight metal-poor stars with metallicities in the range -0.6<=[Fe/H]<=-3.0. Elemental sulphur abundances were derived for six targets, and upper limits were set for two of the most metal-poor stars in the sample. The sulphur doublet at 8694.62 Å has been detected in three stars (HD 19445, HD 2665, and HD 2796) with [Fe/H]<=-1.9. Our observations, combined with those available in the literature, indicate a monotonic increase of the [S/Fe] ratio as [Fe/H] decreases, reaching values of [S/Fe]~0.7-0.8 below [Fe/H]=-2. We discuss plausible scenarios for the interpretation of these results. Based on observations obtained with the William Herschel Telescope (WHT), operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos (ORM) of the Instituto de Astrofísica de Canarias.