WASP-80 is one of only two systems known to contain a hot Jupiter which transits its M-dwarf host star. We present eight light curves of one transit event, obtained simultaneously using two defocussed telescopes. These data were taken through the Bessell I, Sloan g'r'i'z' and near-infrared JHK passbands. We use our data to search for opacity-induced changes in the planetary radius, but find that all values agree with each other. Our data are therefore consistent with a flat transmission spectrum to within the observational uncertainties. We also measure an activity index of the host star of log R '_HK = -4.495, meaning that WASP-80 A shows strong chromospheric activity. The non-detection of starspots implies that, if they exist, they must be small and symmetrically distributed on the stellar surface. We model all available optical transit light curves and obtain improved physical properties and orbital ephemerides for the system.