Wrong - public transport is NOT a statutory public service. It is provided by private companies (apart from the handful of remaining municipal bus companies), and these exist to make a profit. National and local government choose in some instances (rapidly reducing in the case of bus services) to subsidise selected additional services in the public interest, but these wouldn't run if subsidies ceased. Look at what D&G buses are currently doing to their network.
Given the shambles that is currently Northern Rail, they should stop subsidising it and allow the unprofitable lines (probably most of them) to be closed down. It might be worth subsidising selected suburban commuter routes into the major conurbations, to be provided by another operator, in order to assist with reducing road traffic congestion, but rural routes like the Mid Cheshire line passenger service could be closed down completely with minimal impact.
What impact would closing down the MID CHESHIRE line have on the roads? Isn't it true that there are wider economic benefits from running a train service with a subsidy?