Rail infrastructure (Railtrack/Network Rail) and operations (the TOCs) were separated in 1994 in the run up to privatisation.
Network Rail is run and funded on 5-year control periods regulated by ORR, with high level objectives set by government (HLOS/SoFA).
The TOCs are run and funded by franchise agreements of varying durations up to 15 years (25 years for locally-managed Merseyrail), set by government.
The objectives and incentives of each "side" can vary considerably, and can get completely out of sync.
Notable structural failures were West Coast Route Modernisation, the electrification cutbacks, and now the timetable meltdown.
On top of that, the business models on both sides are creaking - Network Rail is seriously underperforming and has a funding crisis, while the TOCs are in a situation where growth is slowing, performance is deteriorating, and the customers are impatient for improvements which seem very difficult to deliver.
While the DfT notionally owns all the issues, and the means to solve them, the legal setup means it cannot simply tell Network Rail and the TOCs what to do.
NR is protected by ORR and its periodic funding settlements, and the TOCs are protected by their franchise agreements.
The challenge is to find a business model that supplies the funding and has fully aligned (if not merged) operational objectives for both infrastructure providers and operators to deliver an improved service (for less than the current £4 billion a year or whatever).
I think the NATS public-private model outlined in #13 is something that might be considered.
It includes external financing, private operator involvement, and national infrastructure operation, within a structure that retains government overall control (just!).