If you want AVGAS you need to make sure you go to one of the airfields that has an AEF or UAS on it - e.g. Benson, Cosford, Leeming, Leuchars, &c. They operate Grob 115E Tutors so will have AVGAS, though the paperwork is nasty. If there's an AEF they will also mostly be open at weekends.
Otherwise comments above are accurate - the MOD waiver is available from HQ STC at RAF High Wycombe (something like 'civil admin' department, I seem to remember).
You will find the phone numbers for Ops at individual bases in the AFE VFR Flight Guide, amongst others. When you ring, persevere: even flying from a RAF flying club, I often encounter total ignorance when I ring for PPR. If the SNCO who answers doesn't understand, ask them to find out and get back to you. You should end up being given a PPR number which you must bring with you (but never quote over the radio). And you will be bottom priority, traffic-wise - I was held off Leeming for 20 minutes once...
Also, make sure you are up to speed with the military circuit pattern and RT. It's in CAP413 and has been discussed on here before.
On price, BTW, I understand that they've been ordered not to undercut 'similar' civilian airfields. When 'similar' means instrument approaches to all runways, lighting, &c &c you can see why it's expensive. Even though you've already paid for it all, out of taxes...
Tim