Yes and currently cover some Metros thus not entirely railway. Name is historical more than anything as they were created by the British Transport Commission by the amalgamation of the previous Big 4 railway police services. Also covered the canals until 1962 according to their Wikipedia entry.
The Metro one is an interesting point, as BTP covers only a handful across the uk:
BTP Covered Metros:
Midland Metro
Croydon Tramlink (though given the nature of the area, the MET would likely be first responders)
London Underground / Docklands Light Railway / Overground / Crossrail.
Strathclyde Subway
Merseyrail
Non BTP Covered Metros and Railways:
Tyne and Wear - Covered by a dedicated unit in Northumbria Police.
Metrolink - Covered by the Transport Unit in Greater Manchester Police.
Edinburgh Trams - Covered I believe by Police Scotland.
Preserved Railways also fall under the non BTP side of things due to the nature of the funding of the BTP.
The BTP certainly has a unique way of being funded, and coverage of who covers what is can largely come down to which local PTE is in charge + what or who the DfT wants. The BTP will in affect, have to bid if it wants to provide security and Policing and can be up against a Home Office Force with a specialist unit or even private companies (though thankfully this isn't often used - though TFL does use the Land Sheriffs to provide security across much of Crossrail - and from experience they can be a bit of a pain in the when dealing with an incident!). Thankfully, with the funding being provided through the railway, the BTP managed to avoid most of the major cutbacks imposed onto the Home Office forces by our wonderful government a few years back.