Over the years since the initial creation of the Festiniog Railway, the standard gauge railways have changed greatly.
For further historic details see the British Rail page.
Following the split of British Rail in the 1990s, the remaining functions of the British Railways Board are now discharged by BRB (Residuary) Ltd. The company is owned by the Government and reports to the Department for Transport.
As a residuary body, the company is responsible for discharging a variety of functions, including obligations in respect of liabilities acquired by British Rail as a major employer over nearly half a century and as a direct result of the privatisation process.
The above 3 paragraphs are taken from the BRB site. However, I believe the "in respect of liabilities acquired by British Rail" would actually cover not only the period of BR's existence, but any liabilities prior to its creation.
Network Rail inherited and owns the operational infrastructure, including the railway tracks, signals, tunnels, bridges, level crossings and most stations, but not the passenger or commercial freight rolling stock. Network Rail took over ownership by buying Railtrack plc, which was in "railway administration", from Railtrack Group plc for £500 million. The purchase was completed on 2002-10-03.
For further details see Wikipedia.
These links show pending Arrivals / Departures from the local Network Rail stations.