If you don't want to stay in HKG for over 24 hours you could also look at CX flights to somewhere else in Europe and connect from there to LHR. I've been looking at flights from SYD to both AMS and LHR for months now and yesterday booked the first leg of our trip that starts in late May next year. We are joining a cruise in Amsterdam and yesterday booked CX J SYD-AMS for May 29. I found that SYD-AMS J flights were only being released each week for flights on Mondays, Tuesdays and Wednesdays but not for any other days. The taxes for SYD-AMS were $A331.28 each. You could consider flying SYD-HKG-AMS and connect with BA for AMS-LHR. CX also fly from HKG to CDG, ZRH etc so you could also check out CX flights from SYD to other European cities as well.
I've also seen SYD-LHR with BA on BA16/BA12 released on most days but the BA taxes are higher and were $A428.76 each when I checked recently. I haven't seen any CX SYD-LHR J award flights released in the months I have been checking flights daily.
Another option is to look at CX SYD-HKG and connect to BA28 or BA32 for HKG-LHR on the same day. We did this a couple of years ago but booked SYD-HKG online and then paid the 5000 point change fee to add HKG-LHR the following week when BA flights were released. You could be lucky and still find a SYD-HKG J flight available with CX on the date the BA flights are released and not have to pay the 5000 point change fee.
When I looked at both at 10am on Sunday 3 June CX released CX110 SYD-HKG for Wed 29 May 2019 and the same day BA released BA28 & BA32 for Thu 23 May. I've just looked and see at 8.16pm today CX still have 2 J seats on CX110 available for Sat 25 May and BA have BA28 & BA32 available for the same day. It is a risk waiting though if you need a definite date as there are no J CX SYD-HKG seats (all when searching for 2 seats) for Fri 31 or Thu 30 showing available, although there is availability for May 28, 27, 25, 24, 23, 22. When I looked at taxes for these flights a couple of weeks ago it worked out at $A179.38 for SYD-HKG on CX110 and $HK345 or approx $A117 for the HKG-LHR BA flight. I see that CX are releasing SYD-HKG a day ahead of SYD-AMS each day. When I looked on Sunday 3 June they released SYD-HKG for Wed 29 May and SYD-AMS for Tue 28 May.