We present the results of a photometric CCD monitoring of the gravitational lens system UM 673 that took place from 1995 to 2000. In total, the doubly imaged quasar (QSO) was observed in the R band during 29 photometric nights, using optical telescopes with dimensions in the range 0.6-1.3 m. We detected a significant variability in the total light of the UM 673 system, that is, in the light of the two QSO images plus the lensing galaxy. With respect to the magnitude of the gravitational lens system at its discovery, in 1986, UM 673 was 0.3 mag brighter. Furthermore, our 1996 December measurements show that between 1995 November and 1997 October the system became even brighter, reaching a magnitude difference of 0.5 mag with respect to its discovery value. We also present R magnitudes and V-R colors of seven field stars situated in the vicinity of the lens, based on a 3.5 month monitoring during the year 2000. Based on observations made with (1) the 60 cm Bochum and the ESO 90 cm Dutch telescopes, at La Silla, Chile, (2) the 1.2 m telescope at Kryonerion Observatory, Greece, (3) the 1.3 m telescope at Skinakas Observatory, Crete, Greece, and (4) the European Space Agency OGS telescope operated on the island of Tenerife by the Instituto de Astrofísica de Canarias in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias.