Thank you all for your interest and fascinating comments and nuggets information e.g. the EPM holding pattern, difference between OSGB36 and WGS84 and radio ranges. Especial thanks to Flap40 for great geometry and DaveReid and Discorde for their research. Belatedly, seeing those pins on the map reminded me of something which I had overlooked, having become fixated on my Epsom Downs theory. I used to live on the west side of Epsom and walked frequently in the former mental hospitals cluster. I vaguely recall a small brick building in the then farmland between West Park and Long Grove Hospitals. Also, I recall, but can't find, mention on local maps of a radio station in this vicinity. After a bit of digging (thank you National Library of Scotland!) I found an OS map published in 1962 showing a small fenced building at TQ 190 620. TQ 19 62 is the whole 1km grid square within DaveReidUK's red oblong so bottom left of that!
I've twice tried to send this post with a JPG of part of the OS map only for it to be rejected for apparently including a URL. Rather than risk it again I'll post the JPG separately.
Thanks again everyone!