Taphappy, there was it seems an RAF Reading and, just as you recall, there seems to have been no stated purpose for it nor named units based at it. However, the co-ordinates given put it close by the railway station and hence probably never "on the outskirts". It seems to have occupied 8 Gun Street! I wonder if that was the "front door" of your place, or more likely perhaps yours went after a completely different ID, named after some hamlet or village around there.
The only airfields around Reading that I could find were RAFs Woodley, Theale, and Smiths Lawn (all 50Gp EFTS) and further out RAF Hampstead Norris (12 Gp OTUs). Do any of those ring a bell?
Stations-R Edited to add, to the East lay RAFs White Waltham, Waltham St Lawrence, , and Bray Court (EFTS), to the North RAF Henley (EFTS), and to the South RAF Shinfield Park (HQ Flying Training Command!)