We use the Hernandez-Perez and Bruzual stellar population synthesis models to study the role of interacting binary pairs as progenitors of extreme horizontal branch (EHB) stars. We assemble a sample of 3417 early-type galaxies observed both in the optical (SDSS-DR8) and the UV (GALEX-GR6). The galaxies in our sample can be classified according to their position in the colour-colour diagram as UV-weak or red-sequence galaxies (~48%), UV-strong or UVX galaxies (~9%), and recent star-forming galaxies (~43%). Analysing this sample using the models for various choices of basic model parameters, we conclude that (a) the UVr colours of UV-weak and UV-strong galaxies are reproduced by the models as long as the fraction of binary stars is at least 15%. (b) Higher metallicity models (Z=0.02 and 0.03) reproduce the colours of UV-weak and UV-strong galaxies better than lower Z models. The Z=0.03 model is slightly bluer than the Z=0.02 model in the UV-strong region, indicating a weak relationship between UVX and Z. (c) The strength of UVX increases with age in the model population. This is at variance with the results of other models that include binary stars as progenitors of EHB stars.