The Kings Fund is a credible source of information about the NHS systems in England, Scotland, Wales, and NI. One of the reasons that they're credible is because they're cautious about definitions. In your quote they're saying "lots of people have written about this, and they all use slightly different definitions for management, and so they all give different numbers".

What is a manager? Are you only including non-clinical staff? Or do clinical staff count too? If you're including clinical staff, how many hours of their working week are you counting as clinical hours and how many are you counting as managerial hours? Are you converting people who work part time as managers to Full Time Equivalent positions, or not?

If you want to poke the data it's here: https://digital.nhs.uk/data-and-information/publications/sta...

If you want more description of the complications of counting managers in the NHS I found these useful (if a bit old now):

https://www.kingsfund.org.uk/publications/future-leadership-...

https://www.kingsfund.org.uk/projects/general-election-2010/...

https://www.kingsfund.org.uk/projects/health-and-social-care...