We report a novel, compact and automated multidimensional spectrofluorometer that exploits a fibre-laser-pumped ultrafast supercontinuum source to provide resolution with respect to intensity, excitation and emission wavelength, decay time and polarisation. This instrument has been applied to study the photophysics of the phase-sensitive membrane probe di-4-ANEPPDHQ and to characterise protein-protein interactions via Förster resonance energy transfer. It can be applied to in situ measurements via a fibre-optic probe in medical and other contexts and is demonstrated here to provide a comprehensive characterisation of tissue autofluorescence.