Almost always conservatives, the key exception in recent history being Tony “Tory Lite” Blair's time in office (who pretty much ignored many years of promises to undo the direction Thatcher and Major had taken NHS and university/student funding should Labour be returned to power, greatly irritating many of us who voted for them that time around). Unfortunately this is a common pattern: parties like Labour get control and realise how hard it is going to be to fight what has been set in motion so do too little or actively push on in the existing direction (just applying a little lipstick to the pig for public appearances). The current lot are trying to do better in that regard, but are failing so impressively elsewhere that they likely won't have a second term and one term is not enough to build momentum, so their replacement will just put a stop to any good that has actually been achieved. The scary thing is that their replacement (assuming Refrom don't rip themselves apart from the inside between now and the next election, which is something there is still hope of happening) might make the old Tories look extremely moderate.
Timetables, expansion any kind of change to rail running is approved centrally in DfT. The private operators are just that, they only run the trains to spec, on the track provided. In some cases they don't even run the stations they stop at.
What is criminal, and why the same mistakes that keep on being made, is that there little apatite or budget to retain expertise in house. This means that the DfT is reliant on consultants for most things.
THis would be fine if the people making the decisions were not people like chris grayling or grant schapps, who have no care for long term issues, only short term career success.
It costs a shit ton more, and there is less accountability. Its basically like asking claude to design the system for you. Sure it appears faster, but in the end it you'll have to redo all of it manually with no context.
The whole great british railway shit is basically just re-branding the regional franchises, and nothing more.
The train operating companies are mostly privately owned but they do not build the infrastructure. Quite a few are state owned though (LNER, Thameslink, Scotrail, Northern...)
Network rail are not building east-west rail, let alone HS2.
The default assumption these days is that everything will be contracted out. It needs a cultural change and a lot of investment to change things.