Before the end of the Epoch of Reionization, the Hydrogen in the Universe was predominantly neutral. This leads to a strong attenuation of Ly alpha lines of z greater than or similar to 6 galaxies in the intergalactic medium. Nevertheless, Ly alpha has been detected up to very high redshifts (z similar to 9) for several especially UV luminous galaxies. Here, we test to what extent the galaxy's local environment might impact the Ly alpha transmission of such sources. We present an analysis of dedicated Hubble Space Telescope (HST) imaging in the CANDELS/EGS field to search for fainter neighbours around three of the most UV luminous and most distant spectroscopically confirmed Ly alpha emitters: EGS-zs8-1, EGS-zs8-2, and EGSY-z8p7 at z(spec) = 7.73, 7.48, and 8.68, respectively. We combine the multiwavelength HST imaging with Spitzer data to reliably select z similar to 7-9 galaxies around the central, UV-luminous sources. In all cases, we find a clear enhancement of neighbouring galaxies compared to the expected number in a blank field (by a factor similar to 3-9x). Our analysis thus reveals ubiquitous overdensities around luminous Ly alpha emitting sources in the heart of the cosmic reionization epoch. We show that our results are in excellent agreement with expectations from the Dragons simulation, confirming the theoretical prediction that the first ionized bubbles preferentially formed in overdense regions. While three UV luminous galaxies already have spectroscopic redshifts, the majority of the remaining fainter, surrounding sources are yet to be confirmed via spectroscopy. JWST follow-up observations of the neighbouring galaxies identified here will thus be needed to confirm their physical association and to map out the ionized regions produced by these sources.