There does seem to be a bit of a consensus regarding the Djinn and Dollar/BEAS.
What we know (according to Planemike) is that the UK Djinns were regesterined to Agricultural Air Services (AAS) who were evidently based at Kidlington and which is presumably a close enough association to assume that there may have been a link with BEAS. As Planemike suggested, there was probably a degree of collaboration between AAS and BEAS.
This photo
Air-Britain : G-AXBX was taken at the back of the hangar BEAS used at Kidlington. The tail of one of their Brantlys is visible. My notes show I saw two of the Djinns there in July 1969 ( that was when you could walk around Kidlington at your leisure).
Planemike