Tridents, and indeed Comets before them, went to all the eastern Med points, most commonly through Nicosia in Cyprus, also served nonstop by both types (Tel Aviv is actually visible on the horizon when you are at altitude over Cyprus). BEA had a longstanding codeshare agreement with Cyprus Airways, who didn't have their own aircraft in the 1960s, on this. The Comets got to Beirut, Cairo, and for a while further, to Damascus, Kuwait, Bahrain and Doha, which are the farthest destinations served by BEA aircraft and crews. I think this 1961 timetable has BEA Comets to all the points mentioned.
http://www.timetableimages.com/ttima...61/be61-17.jpg
and no, BOAC, despite showing many other partners, only sparingly included any such flights in their timetables - and in return BEA never showed BOAC ones in theirs.
Separately to this, BEA in the 1960s provided two Viscount 800s to Cyprus Airways, which did their local regional flights. I believe the BEA square logo in the cheatline (but not the big red one on the fin) was replaced by a CY logo for the duration, which for each of the two aircraft typically lasted for about 3 months before coming back to Heathrow for a check and being replaced.
Once the Comets had gone a Trident was all BEA had for Moscow, loads could be notably thin at times and there are stories of them being down to single figures in winter. Aeroflot ran Tupolev 104s on the route, changing over to Ilyushin 62s around 1970. It was almost unknown for Soviet nationals to be on the BEA flight, despite each only operating on a few days a week. The BOAC 707 Moscow flights were a separate operation through to Tokyo, which started in 1971, the "Russiaway to Japan" route, for which they had to buy two new and specially equipped 707s actually after they started taking delivery of 747s - which were not permitted on the Siberia route for many years afterwards.