Our work investigates the Bose-Einstein condensation of photons in an intra-cavity Mach-Zehnder interferometer with controlled dissipation and feedback. The switching behaviour of the interferometer is analysed in order to reveal the physical mechanisms that control the formation of a Bose-Einstein condensate. We show that by adjusting their frequency, Bose-Einstein condensates naturally seek to minimise particle loss and destructive interference in their environment. The provided dataset contains the experimental data used to generate the figures in M. Vretenar, C. Toebes, J. Klaers, “Modified Bose-Einstein condensation in an optical quantum gas”, arXiv:2105.10708 [cond-mat.quant-gas]. The data consists of grayscale tiff images that describe the photon density in the plane of the microcavity used in this experiment. Furthermore, we provide json files that give integrated intensities derived from these images. Further information can be found in the file README.txt provided with the data set and in the above mentioned publication.