HKG is a nice airport, but there is only that much you can do. You can use the CX F Wing lounge which is a twelve minutes walk from the BA gates, or the QF J lounge which is just 5 minutes away. But the QF lounge downgrades a bit in the evening as most QF flights will have departed.
Both BA flights depart within half an hour. You could use your executive car to arrive two to three hours before departure, check in at BA counters which are to the further right, then walk back to the further left to clear immigration/security and go to the F wing which is just afer immigration to your left.
Or you could directly go to the QF lounge which is near BA checkin and plane. But spending 2 hours at QF lounge is a lot, even if you take a shower.