As I thought, precisely zero facts.
At the time of Privatisation BR had ToUs with MDs & FDs, etc. There were more ToUs than there are TOCs, ergo there are now less of then than there were under BR. Nor, if you go back further were there less managers. My father worked at BR all his life, retiring in the 90s and there were many office buildings that no longer exist. Whole departments (e.g. Work Study) that no longer exist. There are also far less Station Managers than there used to be under BR. There are more driver managers, but that's because there are a lot more drivers. As for Route Directors (or Area Managers as some TOCs use), similar roles existed under BR and will always exist - one Ops or Commercial Director cannot control the whole country.
Unlike you, I have carried out an analysis of manager to staff ratio for some TOCs and it compared very favourably with not only the still publicly owned bits of the railway, but actually with many other industries as well. Also, I saw the changes first hand during privatisation and while there were some small increases in roles such as revenue analysis, there were much bigger cuts in Finance and HR. Since then change (both up and down) has largely been driven by increased services, government requirements and the use of new systems and the same factors would have affected BR, but each time a new franchise competition comes round management roles are scrutinised and savings made. I have twice run HQ departments and on both occasions the numbers were reduced, the first time substantially.
Freight companies are even leaner from what I've seen. Infrastructure companies generally don't just do rail work, so it would be impossible to compare. However, I would be very surprised if they had more managers than BR, simply because BR pretty much never made anybody redundant.