We introduce a new method for determining the influence of galaxies and active galactic nuclei (AGN) on the physical state of the intergalactic medium (IGM) at high redshift and illustrate its potential via a first application to the field of the $z=6.42$ QSO J1148+5251. By correlating the spatial positions of spectroscopically-confirmed Lyman break galaxies (LBGs) with fluctuations in the Lyman alpha forest seen in the high signal-to-noise spectrum of a background QSO, we provide a statistical measure of the typical escape fraction of Lyman continuum photons close to the end of cosmic reionisation. Here we use Keck DEIMOS spectroscopy to locate 7 colour-selected LBGs in the redshift range $5.3lesssim zlesssim 6.4$ and confirm a faint $z=5.701$ AGN. We then examine the spatial correlation between this sample and Ly$alpha$/Ly$beta$ transmission fluctuations in a Keck ESI spectrum of the QSO. Interpreting the statistical HI proximity effect as arising from faint galaxies clustered around the detected LBGs, we translate the observed mean Ly$alpha$ transmitted flux around an average detected LBG into a constraint on the mean escape fraction $langle f_{rm esc}ranglegeq0.08$ at $zsimeq6$. We also report evidence of the individual transverse HI proximity effect of a $z=6.177$ luminous LBG via a Ly$beta$ transmission spike and two broad Ly$alpha$ transmission spikes around the $z=5.701$ AGN. We discuss the possible origin of such associations which suggest that while faint galaxies are primarily driving reionisation, luminous galaxies and AGN may provide important contributions to the UV background or thermal fluctuations of the IGM at $zsimeq6$. Although a limited sample, our results demonstrate the potential of making progress using this method in resolving one of the most challenging aspects of the contribution of galaxies and AGN to cosmic reionisation.
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