Not sure if it was the same for BOAC but I had a family friend that was crew for Qantas in the 70s and he talked of a similar route they did as a round the world trip. Planes didn't do the distances they do now. In 77 I flew SYD/SIN/BOM*/DXB/ATH and the plane went onto ROM (it was on Alitalia). But then saying that we flew back on SQ and I don't recall stopping elsewhere on the way - but then it was a long time ago!
If BOAC did do a RTW sort of trip like QF did, perhaps your father did it due to timing on the dates he needed to fly. I don't know if they had the same frequency of connections as they had today and again, my ex QF crew friend did say that there were some long layovers for crew at some ports as there was only 1 flight per week.