I'm no fan of privatisation of the railways (at least, in the form chosen in the UK), but I think it resulted in one big advantage which has led to improved services - the railways became politcally important again. Governments were quite happy to starve BR of investment and decline was seen as the natural way of things. In later years, I think BR did a pretty decent job for the most part, given the resources available. They delivered quite a few substantial improvements for very little money - Thameslink, Chiltern upgrade, west London line, etc.
After privatisation, having made such high profile changes, governments suddenly saw the railways as important. Subsidy was hugely increased and a lot of public investment flowed. What BR could have achieved with the money, we will never know. Certainly the current system is inefficient in many ways, does not bring in private investment, is inflexible and requires huge and continuous government intervention to operate. But the extra public money and political will have brought improvements and the system is generally in better shape now than twenty years ago.