Protoplanetary discs form and evolve in a wide variety of stellar environments and are accordingly exposed to a wide range of ambient far ultraviolet (FUV) field strengths. Strong FUV fields are known to drive vigorous gaseous flows from the outer disc. In this paper we conduct the first systematic exploration of the evolution of the solid component of discs subject to external photoevaporation. We find that the main effect of photoevaporation is to reduce the reservoir of dust at large radii and this leads to more efficient subsequent depletion of the disc dust due to radial drift. Efficient radial drift means that photoevaporation causes no significant increase of the dust to gas ratio in the disc. We show that the disc lifetime in both dust and gas is strongly dependent on the level of the FUV background and that the relationship between these two lifetimes just depends on the Shakura-Sunyaev $\alpha$ parameter, with the similar lifetimes observed for gas and dust in discs pointing to higher $\alpha$ values ($\sim 10-2$). On the other hand the distribution of observed discs in the plane of disc size versus flux at $850 \mu$m is better reproduced by lower $\alpha$ ($\sim 10-3$). We find that photoevaporation does not assist rocky planet formation but need not inhibit mechanisms (such as pebble accretion at the water snow line) which can be effective sufficiently early in the disc's lifetime (i.e. well within a Myr).