I am not sure the RS refers to Rochester and Strood, as RS can be seen on footpaths all over the country, I think they refer to ancient footpaths rather than the more modern designated ones, I believe they refer back to Norman times, the numbers allocated to them are there just to Identify them, so if you reported a large hole, dumped rubbish etc to the council they would know where it was, a bit like road numbers..
There are several designated abbreviations for footpaths, and they usually denote what sort of traffic is allowed on them for example:
RUPP....Road used as a public path.
PROW...Public right of way.
and many more.
Any footpath used before 1949, and not logged on a map by 2026, will be lost forever
There are several acts that cover these matters, the Countryside Act et al, and several Council Sites which give info regarding rights of way, Bridle paths etc, and a lot too much in my opinion on how landowners can get thee paths removed and closed.
good luck on your quest.