It would appear that Fairoaks Airport Ltd is ultimately owned by an Albemarle company registered in Guernsey. I suspect this is the company which owns the property and takes rents.
There is also Fairoaks Airport (Operations) Ltd, which is owned by Forsters LLP, a large firm of lawyers in London. I suspect this company runs the runway and ATC.
Forsters LLP also appear to own Albemarle Shoreham Airport Ltd, which I believe runs the operational side of Shoreham, whereas Albemarle (Shoreham) Ltd, also owned by Forsters LLP appears to deal with the properties at Shoreham Airport.
I guess it is possible that Forsters may be nominees for others.
All information above available from Companies House