We present models in which the photoevaporation of discs around young stars by an external ultraviolet source (as computed by Adams et al 2004) is coupled with the internal viscous evolution of the discs. These models are applied to the case of the Orion Nebula Cluster, where the presence of a strong ultraviolet field from the central OB stars, together with a detailed census of circumstellar discs and photoevaporative flows, is well established. In particular we investigate the constraints that are placed on the initial disc properties in the ONC by the twin requirement that most stars possess a disc on a scale of a few A.U., but that only a minority ($< 20 %$) are resolved by HST at a scale of 50 A.U.. We find that these requirements place very weak constraints on the initial radius distribution of circumstellar discs: the resulting size distribution readily forgets the initial radius distribution, owing to the strong positive dependence of the photoevaporation rate on disc radius. Instead, the scarcity of large discs reflects the relative scarcity of initially massive discs (with mass $> 0.1 M_\odot$). The ubiquity of discs on a small scale, on the other hand, mainly constrains the timespan over which the discs have been exposed to the ultraviolet field ($< 2 $Myr). We argue that the discs that are resolved by HST represent a population of discs in which self-gravity was important at the time that the dominant central OB star switched on, but that, according to our models, self-gravity is unlikely to be important in these discs at the present time. We discuss the implications of our results for the so-called proplyd lifetime problem.

8 pages, 5 figures, MNRAS accepted