We show that at wavelengths comparable to the length of the shower produced by an Ultra-High Energy cosmic ray or neutrino, radio signals are an extremely efficient way to detect these particles. Through an example it is shown that this new approach offers, for the first time, the realistic possibility of measuring UHE neutrino fluxes below the Waxman-Bahcall limit. It is shown that in only one month of observing with the upcoming LOFAR radio telescope, cosmic-ray events can be measured beyond the GZK-limit, at a sensitivity level of two orders of magnitude below the extrapolated values.