My old house had the one my father-in-law removed from his house and original both houses built within a month of each other, one plastic base other wood base, both populated with MCB's not fuses, and each supplied from its own RCD, so until the CU became metal it was the same protection as modern twin RCD consumer units.
When I added RCD's there were no RCD consumer units, but today it would not be worth the effort adding RCD's easier and likely cheaper to renew the fuse box with a consumer unit.
But as to question bathroom work, it would require RCD protection and having the fuse box replaced would seem the way forward, however first the existing installation needs testing, some one tried to replace the old fuse box at my mothers house, and could not get the RCD to hold in, there were clearly other faults which were not apparent until changed.
I would say if wiring latter than 1966 then likely there will not be problems, if before 1966 then get it all checked first, as it could easy snowball into a big job, rules changed in 1966 which is why I give that date.
