If the bathroom is on the top floor, rewiring the lighting circuit need not be such a job, as the cables are probably clipped to the joists or maybe in steel conduit, and the new ones can be surface clipped, with good access to the holes for the ceiling roses.
If you are reasonably lucky, the switch drops will be in steel conduit which you can re-use, and avoid chasing out the new wallpaper, though you need some kind of gland or other protector on the sharp edge, and unless the conduit is fully buried in the wall and inaccessible, it needs to be earthed.
p.s. No reason why you shouldn't cross-bond all the pipes that enter the bathroom anyway, and to the CPC (earth wire) of anything like an immersion heater or CH pump that may be in the airing cupboard. That will bring them all to the same potential, which is the main object of Bathroom Supplementary Bonding. Presumably the cold water pipe (and the gas pipe) are main bonded as well? If so, and you have copper pipes throughout, you will be bringing in the earth connection for the whole installation. I can't see that would be wrong. Do you know what kind of earth you have at the meter/main fuse/consumer unit?
