One of the thigns that Land Registry will be intereste din if anyone wants to claim adverse possession over a piece of unregistered land is whether the land is occupied to the exclusion of others, including the rightful owner. As the term implies, adverse possession doe sinvolve an element of possessing the land in question!
Basically, what normally happens is the person or body who is in possession of the land will make an application for First Registration based on their occupation of the land. Land Registry will firstly check that the application is in order and that the following criteria have been met:
the squatter has factual possession of the land
the squatter has the necessary intention to possess the land
the squatter’s possession is without the owner’s consent, and
all of the above have been true of the squatter and any predecessors through whom the squatter claims for at least 12 years prior to the date of the application (see section 4 The limitation period).
Source
http://www.landregistry.gov.uk/professional/guides/practice-guide-5
If it appears from the application that these requirements have been met, they will usually arrange for a survey to take place to establish the facts of the matter on the ground.
Should the inspection confirm the facts, Land Registry will seek to serve notice on the rightful owner of the land. Ultimately, issues of ownership may have to be decided by teh Adjudicator to HM Land Registry or by a court. As merlodlliw has said, Land Registry will nott ake sides or decide on disputes itself.
I think the biggest issue here is whether the land in question is being occupied or possessed to a sufficient degree to justify an adverse possession claim on it. If it is merely being marked as a footpath then this suggests t me it has not.
In addition, as others have remarked, it is up to the owner to defend their paper title. A member of the public is not able to do much via the route of land registration unless they can demonstrate a clear legal interest in the land.
As far as the Limitation Period goes, however, as far as I can remember railway land does not fall into any of the special categories of exemption, though I look forward to being corrected if my memory has let me down!