Thanks for all the thoughts. Useful indeed! The background COULD of course be anything at all, including horticultural, but I am now firmly of the conclusion that Mike has it right - MkII Ground Laying Radar.
It appears that many AA batteries had this ground laying radar set-up. It had been established that the best way to get accurate readings of aircraft direction and altitude was to ensure that the area surrounding the detection equipment was flat. To achieve that, huge (130 yard diameter) octagonal ground mats were created covering an area of about 15,000 square yards; these were 2" mesh (chicken wire), they consumed 230 rolls of material (each 4' x 50 yards) and 650 miles of wire and they were elevated some feet from the ground by means of poles. They took a team of 50 men about four weeks to construct. There was transmitting equipment on the edge of the mat and a receiver stuck right in the middle of it. You can just see one of the latter in the middle of the photograph background.
There were hundreds of these at anti-aircraft batteries around the country. The technology was superseded before the end of the war but existing set-ups were kept in operation. Whilst the move of some Home Guards in 1942/43 from normal infantry duties to the manning of AA batteries was usually to the newer "Z" rocket batteries, many men also manned more conventional batteries, including both heavy and light guns. I am pretty sure that this is one of them, operated at least in part by members of the 24th Warwickshire Home Guard.
The question remains, where? A Home Guard is unlikely to have had a battery on his doorstep but is certain to have been directed to one located not too far away. The men worked on a shift pattern, with a large number of men on the roll, and they would have been regularly moved to and from the battery by lorry from assembly points near to their home.
Looking at where AA sites were in Birmingham, three or four (commutable) possibilities come to mind: Swanshurst Park, Yardley Wood; Oaklands and Glebe Farm, both Yardley area; and just possibly Olton Hall. Would all of these have accommodated mature trees in the background at that time?
No opinion on sunglasses, except - has to be unlikely and much more probably the quirk of a not very good print!
Thanks again for the ongoing interest.
Chris
(Sources: Wikipedia, Royal Artillery website etc.)