Headley Court is not owned by the military but by a trust, they will decide the future of the real estate but there is no benefit to MOD from real estate sale. The site also comes with certain limitations, especially with relation to expansion and/or flexibility.
The new site is largely being funded by the Duke of Westminster with MOD picking up the running expenses.
It should provide a state of the art facility at least as good as Headley Court if the most prized asset, the staff, relocate.