Has it fuck. Privatisation was supposed generate sufficient profit to support operation and investment, and thus end the need for the taxpayer to subsidise the railways. The cost to the taxpayer, in paying rail subsidies to the privatised rail companies is now far, far more, in real terms, that it used to cost to fund British Rail. Yet at the same time, passengers have faced sky-rocketing fares.
The only reason there has been an increase in investment is because the roads-obsessed Thatcher government deliberately starved British Rail of funds and, in one transport official's words, purposely put the rail system into a state of "managed decline". Some of the huge fare increases are now being spent on investment, it's true, but the same could have been achieved by keeping British Rail public, keeping fares stable, and putting slightly more public money into the network. Instead, public money is going into the pockets of the directors and shareholders of the franchisees.
The promise was that rail privatisation would remove from the British taxpayer the burden of having to support the railways. That promise has not been delivered on. You can't claim what's happened is "a success".