Here we make a new study of the behaviour of the NaI/KI column density ratio in the interstellar medium, using a sample of new observations of 28 stars obtained at the Nordic Optical Telescope (NOT) in 1996 and 1997, and previously published observations (obtained by some of the authors) of 21 stars. The sightlines cover a range of distances and directions, including into the Galactic halo. We make use of new observations of the NaI ultraviolet (UV) doublet for some 18 stars. This doublet is much weaker than the NaI D doublet and so is less susceptible to saturation effects, and it is well known that it can be used to obtain more accurate NaI column densities with a smaller error range. We find an average N(NaI)/N(KI) ratio from the NaI UV data of about 90, which is rather higher than that found previously by Hobbs and Lequeux. The Na UV-KI ratio shows a small increase in value with increasing column density, while we also find a sample of low N(NaI)/N(KI) ratio clouds generally seen towards distant objects on high-latitude sightlines that reach into the halo, so that the ratio decreases more sharply at lower column densities. As the values of the ratio for these halo clouds (10-20) bracket the cosmic Na/K abundance ratio, we suggest that these ratios result from a harder radiation field in the lower halo, such that the ionized fractions of NaI and KI become similar. Clearly caution needs to be applied in using any kind of `standard value' for the NaI/KI column density ratio.