Aims. ESO 243-49 HLX-1, otherwise known as HLX-1, is an intermediate mass black hole (IMBH) candidate located 8 (3.7 Kpc) from the centre of the edge-on S0 galaxy ESO 243-49. How the black hole came to be associated with this galaxy, and the nature of the environment in which it resides, remain unclear. Using multi-wavelength observations we aim to investigate the nature of the medium surrounding HLX-1, search for evidence of past mergers with ESO 243-49 and constrain parameters of the galaxy, including the mass of the expected central supermassive black hole, essential for future modelling of the interaction of the IMBH and ESO 243-49. Methods. We have reduced and analysed integral field unit observations of ESO 243-49 that were taken with the MUSE instrument on the VLT. Using complementary multi-wavelength data, including X-shooter, HST, Swift, Chandra and ATCA data, we have further examined the vicinity of HLX-1. We additionally examined the nature of the host galaxy and estimate the mass of the central supermassive black hole in ESO 243-49 using (black hole mass)-(host spheroid) scaling relations and the fundamental plane of black hole activity. Results. No evidence for a recent minor-merger that could result in the presence of the IMBH is discerned, but the data are compatible with a scenario in which minor mergers may have occurred in the history of ESO 243-49. The MUSE data reveal a rapidly rotating disc in the centre of the galaxy, around the supermassive black hole. The mass of the supermassive black hole at the centre of ESO 243-49 is estimated to be 0.5−23 × 10 7 M . Studying the spectra of HLX-1, that were taken in the low and hard state, we determine H α flux variability to be at least a factor 6, compared to observations taken during the high and soft state. This H α flux variability over one year indicates that the line originates close to the intermediate mass black hole, excluding the possibility that the line emanates from a surrounding nebula or a star cluster. The large variability associated with the X-ray states of HLX-1 confirms that the H α line is associated with the object and therefore validates the distance to HLX-1.