Published in: Astron. Astrophys. 351 (1999) 433 citations recorded in [Science Citation Index] Abstract: We discuss the statistical properties of faint background galaxies detected in a deep Hubble Space Telescope ultraviolet (F336W) Wide Field Planetary Camera 2 image of the lensing cluster Abell 370 (z=0.37). By combining modelled field galaxy counts at this wavelength with a detailed mass model for the cluster, we develop techniques for predicting the expected redshift distribution of lensed sources and find the bulk of the sources should be moderately magnified sources whose redshifts lie between 0.5 and 2. We compare these predictions with redshift estimates derived from the lens inversion method which utilises the shapes of individua...