Over the years since the initial creation of the Festiniog Railway, the ownership of the standard gauge railways has changed greatly.
The Festiniog and Blaenau Railway was a separate narrow gauge operation, which extended the Festiniog Railway's 2 ft (nominal) gauge to Llan Ffestiniog, and operated from May 1868 to 1883. The Bala and Festiniog Railway, which had bought the F&BR in 1876, was a standard gauge line, that by 1882 had reached Llan Ffestiniog. The F&BR section was then converted to standard gauge and through running commenced September 1883. The B&F was already a puppet of the GWR and was eventually amalgamated with it in 1910.
The line into Blaenau Ffestiniog from the north was originally planned as a narrow-gauge route, but before completion it became part of the London & North Western Railway and was converted to standard gauge before opening. In the "Grouping" of 1922, it became part of the London, Midland and Scottish Railway (LMS).
In 1948, almost all the railway system in the United Kingdom was nationalised, and operated under the general title of British Railways. The branding was later abbreviated to British Rail in order to present a modern image.
With privatisation in the early/mid 1990s, responsibility for the infrastructure went first to Railtrack, a privatised operation, then Network Rail, a semi-governmental operation.
Operation of the trains is in the hands of franchise holders, which change from time to time.
Under the 1993 Railways Act, the old British Rail was split up and sold off. By November 1997, British Rail had been divested of all its operating railway functions.
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.