A large fraction of stars are in binary systems, yet the evolution of proto-planetary discs in binaries has been little explored from the theoretical side. In this paper we investigate the evolution of the discs surrounding the primary and secondary components of binary systems on the assumption that this is driven by photoevaporation induced by X-rays from the respective star. We show how for close enough separations (20-30 AU for average X-ray luminosities) the tidal torque of the companion changes the qualitative behaviour of disc dispersal from inside out to outside in. Fewer transition discs created by photoevaporation are thus expected in binaries. We also demonstrate that in close binaries the reduction in viscous time leads to accelerated disc clearing around both components, consistent with unresolved observations. When looking at the differential disc evolution around the two components, in close binaries discs around the secondary clear first due to the shorter viscous timescale associated with the smaller outer radius. In wide binaries instead the difference in photo-evaporation rate makes the secondaries longer lived, though this is somewhat dependent on the assumed scaling of viscosity with stellar mass. We find that our models are broadly compatible with the growing sample of resolved observations of discs in binaries. We also predict that binaries have higher accretion rates than single stars for the same disc mass. Thus binaries probably contribute to the observed scatter in the relationship between disc mass and accretion rate in young stars.