The recent detection of ULASJ1342+0928 , a bright QSO at z = 7.54 , provides a powerful probe of the ionisation state of the intervening intergalactic medium , potentially allowing us to set strong constraints on the epoch of reionisation ( EoR ) . Here we quantify the presence of Ly \alpha damping wing absorption from the EoR in the spectrum of ULASJ1342+0928 . Our Bayesian framework simultaneously accounts for uncertainties on : ( i ) the intrinsic QSO emission ( obtained from reconstructing the Ly \alpha profile from a covariance matrix of emission lines ) and ( ii ) the distribution of H II regions during reionisation ( obtained from three different 1.6 ^ { 3 } Gpc ^ { 3 } simulations spanning the range of plausible EoR morphologies ) . Our analysis is complementary to that in the discovery paper ( Bañados et al . ) and the accompanying method paper ( Davies et al . ) as it focuses solely on the damping wing imprint redward of Ly \alpha ( 1218 < \lambda < 1230 Å ) , and uses a different methodology for ( i ) and ( ii ) . We recover weak evidence for damping wing absorption . Our intermediate EoR model yields the following constraints on the volume-weighted neutral hydrogen fraction at z = 7.5 : \bar { x } _ { \mathrm { H { \scriptscriptstyle I } } { } } = 0.21 \substack { +0.17 \ -0.19 } ( 68 per cent ) . The constraints depend weakly on the EoR morphology . Our limits are lower than those presented by Bañados et al . and Davies et al. , though they are consistent at \sim 1 – 1.5 \sigma . We attribute this difference to : ( i ) a lower amplitude intrinsic Ly \alpha profile obtained from our reconstruction pipeline , driven by correlations with other high-ionisation lines in the spectrum which are relatively weak ; and ( ii ) only considering transmission redward of Ly \alpha when computing the likelihood , which reduces the available constraining power but makes the results less model-dependent . Our results are consistent with previous estimates of the EoR history , and support the picture of a moderately extended EoR .