BEA most certainly did fly Viscounts (802/806) into Tempelhof. I did a year with them (seconded - on and off) in 1964.
PanAm did not use DC-6s into Tempelhof but they did use DC-6Bs. (In fact, I'm not sure that PanAm ever operated a DC-6 - I know that PANAGRA did). I commuted from Dusseldorf to Tempelhof several times with PanAm in a DC-6B and very comfortable it was too.
Air France of course operated from Tegel (which was built from scratch during the Airlift).
The British (RAF) airfield was at Gatow which is now the site of the Luftwaffe museum.