Someone said that all traces of the listening post at Dingli had disappeared. Obviously not so - or was that a different building?

Different I think. This place belonged to the RAF whilst the other more secretive establishment belonged to the Admiralty.
I've now been told elswhere that this wasn't a radar but the "Homer" beacon.
From Bill Crawford:
The ROYAL NAVY had a signal station at The Tal Pitkal site which is 800 FT above sea level and an RAF Chain Overseas Low Radar unit was also on this site as my Late DAD served on that RAF unit from 1940 till 1943 .
The Navy station was indeed a listening station which I am told arrived at Dingli in 1938 and the first RAF Radar unit arrived on that site in 1939 . the second RAF unit arrived in 1940 and was stationed at the present Golf Ball site .
The building in the picture is now the AFM surveilance unit and it was in the 1950's the Dingli Homer beacon for guiding aircraft to Luqa airfield .
Bill