The Optical Monitor (OM) on-board XMM-Newton obtained optical/ultraviolet data for the XMM-Newton Extended Survey of the Taurus Molecular Cloud (XEST), simultaneously with the X-ray detectors. With the XEST OM data, we study the optical and ultraviolet properties of TMC members, and to perform correlative studies between the X-ray and OM light curves. In particular, we aim to determine whether accretion plays a significant role in the optical/ultraviolet and X-ray emissions. The Neupert effect in stellar flares is also investigated. Coordinates, average count rates and magnitudes were extracted from OM images, together with light curves with low time resolution (a few kiloseconds). For a few sources, OM FAST mode data were also available, and we extracted OM light curves with high time resolution. The OM data were correlated with Two Micron All Sky Survey (2MASS) data and with the XEST catalogue in the X-rays. The XEST OM catalogue contains 2,148 entries of which 1,893 have 2MASS counterparts. However, only 98 entries have X-ray counterparts, of which 51 are known TMC members and 12 additional are TMC candidates. The OM data indicate that accreting stars are statistically brighter in the U band than non-accreting stars after correction for extinction, and have U-band excesses, most likely due to accretion. The OM emission of accreting stars is variable, probably due to accretion spots, but it does not correlate with the X-ray light curve, suggesting that accretion does not contribute significantly to the X-ray emission of most accreting stars. In some cases, flares were detected in both X-ray and OM light curves and followed a Neupert effect pattern, in which the optical/ultraviolet emission precedes the X-ray emission of a flare, whereas the X-ray flux is proportional to the integral of the optical flux.