Let's say in the 50s and 60s, before the oil crisis hit and after they'd had enough time to move past the transitional stage, were the passenger services offered by British Railways cheaper (per mile travelled or per average daily commute of the respective period), safer (accidents/casualties per mile), more efficient, more easily available, and more comfortable than, say, in 1938? What about before the WW1 interventions? I'll be happy with partial answers as well as with answers related to criteria I forgot to include. Edit: typo.
The problem with attempting to answer this question is that any answer will be so hedged about with caveats and complications as to not be able to be clear or unclear as to whether “better” or not can be ascertained.
The railways were taken in national ownership on the first of January 1948. However the this is just two years after the Second World War had ended.
The railways had been under direct government control since September 1939, so to compare nationalised BR with the private companies we would have to go back 9 years earlier. But obviously WW2 was a hugely transformative event for the U.K. with huge growth in manufacturing and in employment. The railways were worked very intensively and at the end of the war there was a huge backlog of maintenance and renewal that would take many years to address, and the government cavilled ( as it had also done after WW1) about recompensing the private companies for the wear and tear and losses. It was cheaper for the government to nationalise and pay compensation to shareholders, although to be clear the commitment to nationalisation was ideological in the new labour government not necessarily pragmatic.
Whatever happened performance of the railways was going to be worse because of deferred maintenance and investment until that could be addressed
The war changed many other things. A particularly important one was motor and lorry use and investment in roads. After the war private car ownership and road haulage grew rapidly eating into passenger and freight levels. The railways went from being profitable to large year on year losses. Again this was nothing to do with nationalisation, but it makes meaningful comparisons before and after the war problematic.