Presented are the results of a large and deep optical-near-infrared multi-epoch survey of the Praesepe open star cluster using data from the UKIRT Infrared Deep Sky Survey (UKIDSS) Galactic Clusters Survey. Multiple colour-magnitude diagrams were used to select potential members and proper motions were used to assign levels of membership probability. From our sample, 145 objects were designated as high probability members (p >= 0.6) with most of these having been found by previous surveys although 14 new cluster members are also identified. Our membership assignment is restricted to the bright sample of objects (Z < 18). From the fainter sample, 39 candidates were found from an examination of multiple colour-magnitude plots. Of these, two have small but significant membership probabilities. Finally, using theoretical models, cluster luminosity and mass functions were plotted with the latter being fitted with a power law of alpha = 1.11 +/- 0.37 for the mass range 0.6 to 0.125M(circle dot) and an assumed cluster age of 500 Myr in the UKIDSS Z photometric band. Likewise taking an assumed cluster age of 1 Gyr we find alpha = 1.10 +/- 0.37. Similar values were also found for the J and K bands. These results compare favourably with the result of Kraus & Hillenbrand (alpha = 1.4 +/- 0.2) but are significantly lower than that of the more recent study conducted by Boudreault et al. (alpha = 1.8 +/- 0.1).