The excitation by electron impact of levels of neon, argon, krypton and xenon atoms that decay by emission of ultraviolet light has been studied as a function of incident energy up to a few eV above the energies of the lowest excited levels. The width (FWHM) of the energy spread of the incident beam was typically less than 30 meV. A crossed-beam interaction region was used and UV photons emitted approximately normally to the electron and gas beam directions were detected by a channel electron multiplier. Precautions were taken to avoid detection of scattered electrons and metastable atoms by the photon detector. The onset positions of the lowest excited levels were used in calibrating the incident energy scales. The energies of resonance structures in the excitation functions could therefore be obtained, and are compared with the results of previous experiments.