I did something akin to this about 5 years ago at Middle Wallop. Granted, I was based there at the time, but all I had to do was get permission from the CO and Airfield Manager and ensure that the A/C had the required insurance. I used the local flying club's fuel (which was about 10p per litre cheaper than civvy airfields) and there were no landing fees.
At the time, you could also set up what amounts to an account with the MOD where you have a set number of airfields around the country that you could draw fuel from. All in all, a complete winner.
As I said above, this was about 5 years ago, but the perk was definately worth the considerable amount of paperwork and phone calls that it took to set it up. From memory, it was an individual at Strike who administered the process for all Mil airfields and for all 3 Services.