Caesium silver bismuth halide double perovskites, in the first instance Cs2AgBiBr6, were recently introduced to the field of emerging photovoltaics as environmentally friendly, non-toxic and thermodynamically stable photoabsorber materials. However, the wide indirect bandgaps of these materials indicate the need for bandgap engineering and enhancing the light absorption to improve the photovoltaic performance. The present work demonstrates that this can be achieved via modification of the double perovskite with sulphide to obtain caesium silver bismuth sulphobromide materials, Cs2AgBiBr6-2xSx, which have been synthesised as pin-hole-free uniform films and systematically investigated herein. Notable enhancements in the intrinsic light absorption for 0 ≤ x ≤ 0.2 are demonstrated, as are the improvements by up to 50% in the photocurrent density of the corresponding thin-film solar cells. The devices based on the films with the nominal composition Cs2AgBiBr5.8S0.1 delivered a short-circuit current density of 3.0 ± 0.3 mA cm-2 and a power conversion efficiency of 1.9 ± 0.1% (cf. 2.1 ± 0.2 mA cm-2 and 1.3 ± 0.1%, respectively, for the control cells based on the sulphide-free Cs2AgBiBr6). Equally important, caesium silver bismuth sulphobromides demonstrate excellent stability against all common environmental stimuli, viz. heat, light, and humidity.