Re: "improve productivity in an organisation severely short of staff"
The world's eighth largest employer is not short of staff, severely or otherwise.
https://en.wikipedia.org/wiki/List_of_largest_employers
Whether those staff are competent, productive and needed is a far more relevant question, the answer to which is only ever occasionally 'yes'.
Perhaps addressing the 47.2% of the NHS workforce that aren't in a clinical role might free some of the ever increasing NHS funding to better support healthcare outcomes. Seriously, we really don't need (yet another) £90k/year Head of Diversity and Inclusion (to cite just one vacancy currently being advertised).