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We introduce a new method for determining the influence of galaxies andactive galactic nuclei (AGN) on the physical state of the intergalactic medium(IGM) at high redshift and illustrate its potential via a first application tothe field of the $z=6.42$ QSO J1148+5251. By correlating the spatial positionsof spectroscopically-confirmed Lyman break galaxies (LBGs) with fluctuations inthe Lyman alpha forest seen in the high signal-to-noise spectrum of abackground QSO, we provide a statistical measure of the typical escape fractionof Lyman continuum photons close to the end of cosmic reionisation. Here we useKeck DEIMOS spectroscopy to locate 7 colour-selected LBGs in the redshift range$5.3\lesssim z\lesssim 6.4$ and confirm a faint $z=5.701$ AGN. We then examinethe spatial correlation between this sample and Ly$\alpha$/Ly$\beta$transmission fluctuations in a Keck ESI spectrum of the QSO. Interpreting thestatistical HI proximity effect as arising from faint galaxies clustered aroundthe detected LBGs, we translate the observed mean Ly$\alpha$ transmitted fluxaround an average detected LBG into a constraint on the mean escape fraction$\langle f_{\rm esc}\rangle\geq0.08$ at $z\simeq6$. We also report evidence ofthe individual transverse HI proximity effect of a $z=6.177$ luminous LBG via aLy$\beta$ transmission spike and two broad Ly$\alpha$ transmission spikesaround the $z=5.701$ AGN. We discuss the possible origin of such associationswhich suggest that while faint galaxies are primarily driving reionisation,luminous galaxies and AGN may provide important contributions to the UVbackground or thermal fluctuations of the IGM at $z\simeq6$. Although a limitedsample, our results demonstrate the potential of making progress using thismethod in resolving one of the most challenging aspects of the contribution ofgalaxies and AGN to cosmic reionisation.

The Role of Galaxies and AGN in Reionising the IGM - I: Keck Spectroscopy of 5 < z < 7 Galaxies in the QSO Field J1148+5251