A bit late for your August trip, but RAF Cottesmore do accept civil movements with 24 hour PPR and you need to fax the releavant Insurance paperwork through beforehand (as Fujiflayer says).
IIRC it is also the RAF policy at the moment to welcome civil moves with open arms as a form of revenue and for good
PR.
You will find the mil alot cheaper than most aerodromes and my friend that used Cottesmore was extremely happy with the service.
Melton is about a 15 - 20 min drive from Cottesmore so it may be an option for future reference.