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Ryannnnnn Years ago I would have disagreed with you about nationalising industries and the public services, but not now.
Despite interference by governments and the Treasury often taking too much of the operating profits (as happened to British Railways), so damaging investment, by and large they worked, were cohesive and coherent; and all the profits - or losses - stayed in the country and safe from the panicky ignorami in Canary Wharf and Wall Street.
Network Rail is still UK state-owned. So are the Cross-Country Trains (SW England - NE England - Scotland), much of the UK's goods-train services and licensing the steam-hauled charter trains... only the State in question is Germany.
Just as anything EDF is State-owned - by France.
I doubt the fares would be any lower though. Railways are undeniably very expensive to build, maintain and operate to the standards we demand; and the more they have to do to meet those the costlier they become. You want a £50 fare for that £100 journey? Then expect £50-worth engineering standards of track and rolling-stock, and £50-worth speeds.
Some people fondly compare unfavourably British rail fares etc. with those in a few other countries. Comparisons like that are almost always spurious though. They ignore the problems of course they have there, the very different national economies and travelling patterns, and their far higher subsidies from taxes.
Yes - I think the railways should be state-owned and be using equipment built in Britain, not imported from Japan even if as kits or licence-designs merely assembled here. They should though be run by skilled Chartered Engineers and business managers; not politicians.
(I looked up HS2 once: not a single Engineer on its Board, but it has a 'Director of Strategic Partners' or something equally waffly - so that's all right then. Who would run the HS2 trains? The First Group, apparently, an absolute money-mill whose shares are worth about £90 each. It already owns several rail franchises and the Docklands Light Railway, under false badges. It also owned America's Greyhound Bus company for a while.)
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An incident from 3 years ago:
Travelling from the North of England I needed to be in Bristol early enough for the third of my 3-train journey. We were delayed badly at Leeds by the services' previous train having broken down further North, blocking the path.
You and I are rare nowadays by knowing nothing can ever be guaranteed never to break down unexpectedly, but this was worrying for my trip.
Seeking advice on alternative routes, I asked the staff member why they can't simply shanghai the nearest heavy freight locomotive to draw the breakdown to a safe station where the passengers can alight and wait for the next, and other trains can pass. As used to be feasible.
He replied:
"None of the couplings and so on are compatible any more, like they used to be."
Then he added, "That's privatisation for you!"