In the ultraviolet (UV), Type Ia supernovae (SNe Ia) show a much larger diversity in their properties than in the optical. Using a stationary Monte Carlo radiative transfer code, a grid of spectra at maximum light was created varying bolometric luminosity and the amount of metals in the outer layers of the SN ejecta. This model grid is then compared to a sample of high-redshift SNe Ia in order to test whether the observed diversities can be explained by luminosity and metallicity changes alone. The dispersion in broad-band UV flux and colours at approximately constant optical spectrum can be readily matched by the model grid. In particular, the UV1 − b colour is found to be a good tracer of metal content of the outer ejecta, which may in turn reflect on the metallicity of the SN progenitor. The models are less successful in reproducing other observed trends, such as the wavelengths of key UV features, which are dominated by reverse fluorescence photons from the optical, or intermediate-band photometric indices. This can be explained in terms of the greater sensitivity of these detailed observables to modest changes in the relative abundances. Specifically, no single element is responsible for the observed trends. Due to their complex origin, these trends do not appear to be good indicators of either luminosity or metallicity.