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ABSTRACT Most stars are born in the crowded environments of gradually forming star clusters. Dynamical interactions between close-passing stars and the evolving ultraviolet radiation fields from proximate massive stars are expected to sculpt the protoplanetary discs (PPDs) in these clusters, potentially contributing to the diversity of planetary systems that we observe. Here, we investigate the impact of cluster environment on disc demographics by implementing simple PPD evolution models within N-body simulations of gradual star cluster formation, containing 50 per cent primordial binaries. We consider a range of star formation efficiency per free-fall time, $$\epsilon _{\rm ff}$$, and mass surface density of the natal cloud environment, $$\Sigma _{\rm cloud}$$, both of which affect the overall duration of cluster formation. We track the interaction history of all stars to estimate the dynamical truncation of the discs around stars involved in close encounters. We also track external photoevaporation of the discs due to the ionizing radiation field of the nearby high- and intermediate-mass ($$\gt 5\,{\rm M}_\odot$$) stars. We find that $$\epsilon _{\rm ff}$$, $$\Sigma _{\rm cloud}$$, and the presence of primordial binaries have major influences on the masses and radii of the disc population. In particular, external photoevaporation has a greater impact than dynamical interactions in determining the fate of discs in our clusters.