Using a hybrid binary population synthesis approach, we modelled the formation and evolution of populations of accreting white dwarfs (WDs) for differing star formation histories. We found that the delay time distribution of SNe Ia in the single degenerate scenario is inconsistent with observations. Additionally, we found that our predicted X-ray and UV emission of populations of accreting WDs are consistent with the X-ray luminosities of early-type galaxies observed by Chandra and the HeII 4686 Å/Hβ line ratio measured in stacked SDSS spectra of passively evolving galaxies. Moreover, we found that the majority of current novae in elliptical-like galaxies have low-mass WDs, long decay times, long recurrence periods and are relatively faint. In contrast, the majority of current novae in spiral-like galaxies have massive WDs, short decay times, short recurrence periods and are relatively bright. Our predicted distribution of mass-loss timescales in an M31-like galaxy is consistent with observations for Andromeda.