I don't think there is a viable solution for the railways. The current half-solution isn't working very well, it's taking Network Rail decades to upgrade ageing infrastructure, and even to the point that they abandon projects half-way through (SW electrification).
The problem i see is that if we fully privatise the TOC's and the infrastructure, sure this may generate competition between TOC's operating on popular lines (London), but the rest of the country will likely get forgotten about - or services will likely be awful. The rail-users are then at the mercy of TOC's pricing, as they will likely be able to charge what they wish.
I also can't see how you can force whichever company will own the infrastructure to regularly plough in money for maintenance and future upgrade to the tracks and stations. They will want to maximise profit by doing as little as possible.
Then on the other hand, full nationalisation means the burden falls to the tax-payer. Whilst that might mean rail-users are protected from sharp price hikes, it does mean that the running and large scale projects are unlikely to be as efficient as if they were running under a private company.
The rail network is a complete mess, and i just can't see any options they have of moving it into a self-sustaining model, that can continuously grow and reinvest in itself.