We describe the construction of catalogues of galaxy clusters from the APM Galaxy survey using an automated algorithm based on Abell-like selection criteria. We investigate the effects of varying several parameters in our selection algorithm, including the magnitude range and radius from the cluster centre used to estimate the cluster richnesses. We quantify the accuracy of the photometric distance estimates by comparing them with measured redshifts, and we investigate the stability and completeness of the resulting catalogues. We find that the angular correlation functions for different cluster catalogues are in good agreement with one another, and are also consistent with the observed amplitude of the spatial correlation function of rich clusters.