The Defence Fire Training and Development Centre is under Army administration. The way I understand it is they are responsible for the overall running of the school and the courses for themselves and the RAF, this includes uniformed service personnel and uniformed civilians employed under their umbrella.
The RAF also do their aircraft specific courses on the same site.
It appears that any appropriate fire outfit wanting to put their personnel through various courses there can do so.
the Navy do general fire fighting courses at Portsmouth, and aircraft related courses at Culdrose/Predannack.