Context. Around 10(5) strongly lensed galaxies are expected to be discovered with upcoming wide-field surveys such as Euclid and the LSST. Utilising these large samples to study the inner structure of lens galaxies requires source redshifts, which are needed to turn lens models into mass measurements. However, obtaining spectroscopic source redshifts for large samples of strong lenses is prohibitive with the current capacity of spectroscopic facilities. Aims. As an alternative to spectroscopy, we study the possibility of obtaining source photometric redshifts (photo-zs) for large samples of strong lenses. We pay particular attention to the problem of blending between the lens and the source light.Methods. Our strategy consists of deblending the source and lens light by simultaneously modelling the lens galaxy and the background source in all available photometric bands, and then feeding the derived source colours to a template-fitting photo -z algorithm. We describe the lens and the source light with a S & eacute;rsic profile, and the lens mass with a singular isothermal ellipsoid. We first test our approach on a simulated sample of lenses. Then, we apply it to 23 real systems with broad-band photometry from the Hyper Suprime-Cam survey.Results. We identify the deviations of the lens light from a S & eacute;rsic profile and the contrast between the lens and source image as the main drivers of the source colour measurement error. Although the former is challenging to measure directly for real lenses, we find the latter to be sufficient for evaluating the accuracy of a measured source colour. We split the real sample based on the ratio lambda of the lens to source surface brightness measured at the image locations. In the lambda < 1 regime, the photo -z outlier fraction is 20%, and the accuracy of photo -z estimation is limited by the performance of the template-fitting process. In the opposite regime, the photo -z outlier fraction is 75%, and the errors from the source colour measurements dominate the photo -z uncertainty.Conclusions. Measuring source photo-zs for lenses with lambda < 1 poses no particular challenges compared to the isolated galaxy case. For systems with significant lens light contamination, however, improvements in the description of the surface brightness distribution of the lens are required: a single S & eacute;rsic model is not sufficiently accurate.