133P/Elst-Pizarro is an object that has been described as either an active asteroid or a cometary object in the main asteroid belt. Here we present a photometric and polarimetric study of this object in an attempt to infer additional information about its origin. With the FORS1 instrument of the ESO VLT, we have performed during the 2007 apparition of 133P/Elst-Pizarro quasi-simultaneous photometry and polarimetry of its nucleus at nine epochs in the phase angle range 0 - 20 deg. For each observing epoch, we also combined all available frames to obtain a deep image of the object, to seek signatures of weak cometary activity. Polarimetric data were analysed by means of a novel physical interference modelling. The object brightness was found to be highly variable over timescales <1h, a result fully consistent with previous studies. Using the albedo-polarization relationships for asteroids and our photometric results, we found for our target an albedo of about 0.06-0.07 and a mean radius of about 1.6 km. Throughout the observing epochs, our deep imaging of the comet detects a tail and an anti-tail. Their temporal variations are consistent with an activity profile starting around mid May 2007 of minimum duration of four months. Our images show marginal evidence of a coma around the nucleus. The overall light scattering behaviour (photometry and polarimetry) resembles most closely that of F-type asteroids.