Not easy, but the best way to do it is to think through your flights as if they were all taking place on Sydney time and try to sleep accordingly. In this case for your outbound (if my math is correct, which it probably is not)..

MAN 0410 LON 0510
LON 0835 SIN 2145
SIN 2310 SYD 0655

Ideally, in a perfect world, I would try to get on the Sydney schedule the day of the flight by sleeping in as late as possible and then staying up for the entirety of the MAN-LON-SIN flights before sleeping on SIN-SYD. In reality, that might not be practical, but I find that I can get closer to being on Aussie time that way.