We have a privatised railway.
Really? This is news to me.
All the stations, track, signals, civil engineering (bridges, tunnels etc.) are owned by a state-owned monopoly.*
All the franchises are specified (in terms of service levels, where they serve, a variety of quality measures, and high level requirements like fleet replacement) by DfT.
The franchises that DfT grants are too short to invest in anything long term, without taking on undue risk (regarding lots of investment in rolling stock, which might not have a future home; or in ambitious revenue forecasts, which might not be met because of factors outside your control (Network Rail, the economy, etc.)). Because of this, the returns are paltry (and risky) and there is much less attraction for private companies - hence foreign state ownership of many of Britain's TOCs.
All the fare rises are regulated by DfT, and the fares structure is enshrined in some pre-privatisation rules that no-one dares tamper with. The government effectvely sets fare increases, for the TOCs to take the blame.
The rolling stock is privately owned, but the constraints of moving it around / dependencies on DfT and Network Rail plans etc. mean that the 'market' is not that flexible.
So what we have is a railway that really is not privatised, but just looks that way to the uninitiated. Rather conveniently that allows the DfT / government to avoid blame / responsibility, and the train operators to cop all the blame. Cue a completely uninformed media and politics 'debate' about nationalisation.
It really isn't privatised; it's some horrible halfway house between being privatised and nationalised.
*Yes, I know a couple of stations and one stretch of line aren't, but you get the point.