Individual multiwall boron nitride nanotubes with diameters from 30 nm to 110 nm are shown to be efficient UV emitters by cathodoluminescence. Their luminescence does not evolve much in this diameter range, with dominant UV recombinations at about 230 nm. As a result, single nanotube properties can be obtained from experiments performed on ensembles of nanotubes. Such ensembles are studied by photoluminescence as a function of temperature (5 K-300 K) and by photoluminescence excitation experiments at 9 K. The results are discussed and compared with the related bulk material, hexagonal boron nitride. The strong luminescence recorded around 230 nm is attributed to excitonic effects, more precisely to excitons bound to the structural defects: dislocations, facets, which are observed along the walls.