The problem is that competition on railways, in general, does not work. They tried it in 1825 on the Stockton-Darlington, found it didn't work. Since then the vast majority of operations throughout the world have been vertically integrated. Even the Tories realised this and abandoned their original plans for a free for all privatisation which they found were unworkable.
I wasn't strictly suggesting operations not be virtually integrated, merely I was saying that putting franchises into public ownership while allowing open-access operators like Grand Central to carry on to the same extent as they do now. It's not the same as what you seem to describe as a free for all privatisation.
Newsflash! Pretty much all rail investment already comes from government. Franchisees invest very little. No matter what system is put in place, government decisions will always make or break the railway. A non-ideological government looking to save money would probably nationalise to get rid of the gross inefficiencies of running a fragmented system.
Indeed most subsidies come from the state, but there's nothing to stop a future government deciding it doesn't wish to invest in the railways to such extent anymore. Whoever actually provides the subsidies also has the power to withdraw those subsidies, and there isn't really anyone who can stop them from doing so. I can't imagine Labour would be able to stop the Conservatives from cutting the budget so drastically. After all, they've been powerless against years of austerity, though to be fair they did sometimes go along with it, and I believe an idea of "austerity-lite" was in the minds of some Labour MPs. Regarldess, even if the states chooses to save money by re-nationalising, what's to stop them cutting the budget in the name of saving even more money? Don't get me wrong, I'm in favour of nationalisation, or at least unifying the system, but there's some problems that come with it of course that we must acknowledge and maybe discuss how to come around them.
MTR is a private company?
Not sure if you're being a bit funny there (sorry, I know I'm a bit paranoid), but if you aren't... then yes, MTR is (sort of) a private company. It is a Public company in that it allows members of the public to buy shares on the stock market, but it's otherwise a private company (Public doesn't always mean public sector, though interestingly the Hong Kong Government (specifically The Financial Secretary Incorporated) is a 75.09% owner). It has contracts to run operations not only in London, but also Stockholm, Beijing, Shenhzen, Hangzhou, Melbourne and Sydney. Plus, MTR also runs Hong Kong's rapid transit system, which isn't really a surprise since it's a company based in Hong Kong and listed on their stock exchange. Such experience qualifies it to run Crossrail if you ask me.