I've done this trip more times than I care to remember, mostly in Y.
I find a decent short-ish sleep soon after the first meal, wake up "early", followed by a refreshing shower in the lounges (there's both the QF and BA lounge next door to each other), and the maximise the sleep on the SIN-LHR sector. Usually I manage to stay up most of the day in Australia to about 15:00 in this way.
On the return to UK I've yet to find a routine that works for me.