ABSTRACT Binary stars often move through an ambient medium from which they accrete material and angular momentum, as in triple-star systems, star-forming clouds, young globular clusters, and in the centres of galaxies. A binary form of Bondi–Hoyle–Lyttleton accretion results whereby the accretion rate depends on the binary properties: the stellar masses and separation, and the relative wind speed. We present the results of simulations performed with the hydrodynamic code gandalf, to determine the mass accretion rates over a range of binary separations, inclinations, and mass ratios. When the binary separation is short, the binary system accretes like a single star, while accretion on to stars in wide binaries is barely affected by their companion. We investigate intermediate-separation systems in some detail, finding that as the binary separation is increased, accretion rates smoothly decrease from the rate equal to that of a single star to the rate expected from two isolated stars. The form of this decrease depends on the relative centre-of-mass velocity of the binary and the gas, with faster-moving binaries showing a shallower decrease. Accretion rates vary little with orbital inclination, except when the orbit is side-on and the stars pass through each others’ wakes. The specific angular momentum accretion rate also depends on the inclination but is never sufficient to prevent the binary orbit from contracting. Our results may be applied to accretion on to protostars, pollution of stars in globular and nuclear clusters, and wind mass transfer in multiple stellar systems.