The ATC can own and operate an aircraft - a local SQN to me has a motor glider which they use to give cadets extra flying time.
The ATC is also a charity.
To operate out of Abingdon (i assume from your location,which is 612VS) you would need Crown Indemnity on your aircraft to fly it out of Abingdon.
Where my VGS is based, we have a chap who keeps his condor there and all his mates come and fly it - I don't think you need to become an FTO...but don't quote me! Non of his mates are military.