We describe a technique to search for variability in faint X-ray sources, based on Poisson statistics. This is applied to data in the field of the detached white dwarf binary RE J1629+781 which has been observed repeatedly with the ROSAT Position Sensitive Proportional Counter (PSPC) over a period of 2.5yr as part of the calibration programme of the co-aligned extreme ultraviolet (EUV) sensitive Wide Field Camera. The field contains eight other identified sources comprising four active galactic nuclei (AGN), a LINER, a probable cluster of galaxies and two stars. Variability is detected in three of the AGN, which all have redshifts between 0.35 and 0.38. The amplitude of variability ranges between one and three times the mean count rate, but is only detected on time-scales of less than 3-5 months. No variability is found in the fourth AGN which is at a redshift of 1.1, nor in the LINER galaxy, Arp 185. The X-ray emission from Arp 185 is relatively bright, and the upper limit to flux variations is 27 per cent of the mean flux. This result is consistent with a non-AGN origin for the X-ray emission from this galaxy. Variability is detected from one of the identified stars in the field, of spectral type dM5.5e. No variations were seen in the flux of the other star (spectral type G) or from the probable cluster of galaxies.