Few other local-ish options.
Oxford has quite a few GA aircraft but shares there seem to be like hens teeth.
Hinton mostly LAA stuff there; shares come up occasionally
Gloucester is good for shares, depends where you are in relation to Enstone (it's a bit too far for me)
Bicester has a lot of vintage stuff (Plus my shared Robin DR400), shares pop up occasionally
Turweston also good for shares.
There's occasionally interest in setting up an IFR equipped tourer group in Oxfordshire on these forums but nothing's come of it yet (I'm holding back for the time being until the BIR works itself out, as that's my main driver to upgrade)
Gloucester, Turweston both have active "clubs" - go have a look on the notice boards