Apart from the lack of range, the reason for multi stop services to Australia is that there was insufficient UK-Australia traffic to fill the aircraft
This is actually still the case, certainly for a daily operation, and adds to the other reasons why a 777LR nonstop operation would not succeed. Although London is dominant at the UK end, the traffic spreads across multiple ports in Australia, with even Sydney well under 50% of the total, all of which favours Multiple UK - ME3 hub - Multiple Australian operations.
I know that the Empire service was day time flying only.
Actually they did fly at night, particularly taking off before dawn, using a "flare path" of floating kerosene lamps anchored in the water. Night-time takeoffs were more straightforward in the boats than landings. As significant was that the same crew stayed with the aircraft for several days at a time, and needed a night's rest. They commonly slipped crews just a couple of times, maybe Karachi and Singapore.
Here's some old timetables :
1939 Imperial Airways
http://www.timetableimages.com/ttima...s/iaw39u-2.jpg
1947 BOAC. A tremendously fast, and long-legged, service for its time, by converted Lancaster bomber, only 4 stops to Sydney in 3.5 days.
http://www.timetableimages.com/ttima...47/ba47-05.jpg
1958 BOAC Bristol Britannia and Qantas Lockheed Constellation. Both operators could now take you either way. More stops though than in 1947
http://www.timetableimages.com/ttima...58/ba58-02.jpg
1971, last year of VC10 and 707 monopoly before the widebodies.
http://www.timetableimages.com/ttima...71/ba71-36.jpg