I have here in my collection the BOAC timetable for August 1952 which I think could answer these points.
Singapore airport was still Kallang then. BA (their flight prefix even then) had 4 Canadair Argonauts a week from London, plus 2 a week from Hong Kong, and also 3 faster Lockheed Constellations a week going through to Australia.
The outbound timetable for the Connies, flight BA 704, was:
London 0930 Day 1
Zurich 1200/1300
Beirut 2130
....Nightstop
Beirut 0945 Day 2
Karachi 2030/2300
Calcutta 0530/0645 Day 3
Singapore 1545
....Nightstop
Singapore 0800 Day 4
Jakarta 1030/1130
Darwin 2000/2245
Sydney 0700 Day 5
Cairo (and many other points) were done by the Argonaut schedules.
All times local. Baggage allowance 30 kgs to Singapore, 40 kgs if going through to Australia.
Fare London to Singapore £ 352/16 shillings return. One class only.
The same timetable has the new Comet 3 times a week to Johannesburg, while there are 22 transatlantic flights a week, Stratocruisers and Constellations. The BOAC fleet was very mixed at this time, there are even a few Hermes still about. I suspect you remember the Stratocruisers from the transatlantic sectors.
Earlier timetables in my collection still have the Far East route done by flying boats !
edwardh1, PM me if you would like a scanned image of the timetable when I get back to the UK in a week's time.