We present improved results of the measurement of the correlation between galaxies and the intergalactic medium ( IGM ) transmission at the end of reionisation . We have gathered a sample of 13 spectroscopically confirmed Lyman-break galaxies ( LBGs ) and 21 Lyman- \alpha emitters ( LAEs ) at angular separations 20 ^ { \prime \prime } \lesssim \theta \lesssim 10 ^ { \prime } ( \sim 0.1 - 4 pMpc at z \sim 6 ) from the sightlines to 8 background z \gtrsim 6 quasars . We report for the first time the detection of an excess of Lyman- \alpha transmission spikes at \sim 10 - 60 cMpc from LAEs ( 3.6 \sigma ) and LBGs ( 3.1 \sigma ) . We interpret the data with an improved model of the galaxy-Lyman- \alpha transmission and two-point cross-correlations which includes the enhanced photoionisation due to clustered faint sources , enhanced gas densities around the central bright objects and spatial variations of the mean free path . The observed LAE ( LBG ) -Lyman- \alpha transmission spike two-point cross-correlation function ( 2PCCF ) constrains the luminosity-averaged escape fraction of all galaxies contributing to reionisation to \langle f _ { esc } \rangle _ { M _ { UV } < -12 } = 0.10 _ { -0.05 } ^ { +0.17 } ( 0.18 _ { -0.06 % } ^ { +0.52 } ) . We investigate if the 2PCCF measurement can determine whether bright or faint galaxies are the dominant contributors to reionisation . Our results show that a contribution from faint galaxies ( M _ { UV } > -20 ( 2 \sigma ) ) is necessary to reproduce the observed 2PCCF and that reionisation might be driven by different sub-populations around LBGs and LAEs at z \sim 6 .