For those uncertain about the current timetable here it is :
Singapore - 2320
Heathrow - 0525/1100
Singapore - 0740
Singapore - 2030
Sydney - 0700/0850
Singapore - 1345
Therefore three aircraft are required, two for the London route and one for Sydney. There is no logical service throughout from London to Sydney, directly connecting flights are on other 747 services. When summer time comes in these times change by minutes but the basic pattern is the same as far into the future as Singapore Airlines currently schedule.