The article deals with the detection efficiency of UV-photon detectors consisting of Thick Gas Electron Multipliers (THGEM) coated with CsI photocathode, operated in atmospheric Ne/CH4 and Ne/CF4 mixtures. We report on the photoelectron extraction efficiency from the photocathode into these gas mixtures, and on the photoelectron collection efficiency into the THGEM holes. Full collection efficiency was reached in all gases investigated, in some cases at relatively low multiplication. High total detector gains for UV photons, in excess of 10^5, were reached at relatively low operation voltages with a single THGEM element. We discuss the photon detection efficiency in the context of possible application to RICH.