The only sure way is to examine the Definitive Map for each Council area you are enquiring about, as that is the only full, legal listing of all Public Rights of Way, in conjunction with listing provided by Network Rail. OS actually state on their maps that they may not always be correct.
However you need to beware of even that. Some Rights of Way across railway land also depend on the wording of the original Enabling Acts for that railway. There are quite a number where the RoW ends at the railway boundary and restarts on the other side, and the bit across the railway is actually a Permissive Path.