  Recent evidence supporting reionisation ending at redshift z<6 includes the
rapid redshift evolution of the mean free path for Lyman-limit photons through
the intergalactic medium at 5<z<6. Here we investigate the mean free path
predicted by the Sherwood-Relics suite of hybrid radiation hydrodynamical
simulations. Simulations with comoving volumes of 40^3 h^-3 cMpc^3 (160^3 h^-3
cMpc^3), calibrated to match the observed Lyman-alpha forest transmission with
a late end to reionisation at z<6, are consistent with recent mean free path
measurements at z<5.9, and are 1.2\sigma (1.8\sigma) above the highest redshift
mean free path measurement at z=5.93. The majority of the Lyman-limit opacity
at the end of reionisation is attributable to highly ionised Lyman-alpha forest
absorbers with neutral hydrogen column densities N_HI=10^16--10^17 cm^-2.
Resolving these systems is critical for capturing the redshift evolution of the
mean free path during the final stages of reionisation. After reionisation
completes, overdense gas will reduce the mean free path by up to 20 per cent
around haloes with masses M_h ~ 10^9--10^11 h^-1 M_sol, but during reionisation
ionised bubbles will instead boost the mean free path around haloes by up to an
order of magnitude when the IGM is as much as 90 per cent neutral by volume.
This effect will play an important role in the visibility of Lyman-alpha
emitting galaxies at z>10 discovered with JWST.
