Well, assuming you want to go LHR-SIN-SYD and return SYD-HKG-LHR without other stops or diversions, your options are pretty limited - especially if you want to stick to oneworld carriers so that you'll get BA miles.
If price is no object, it's pretty hard to beat Singapore Airlines business class on the A380 for LHR-SIN-SYD. But that won't get you back through HKG.
Cathay is certainly pretty good, although some find the new business-class herringbone layout of mini-cabinettes a bit claustrophobic and difficult to get in and out of. I found it weird at first, but it's great for privacy and sleeping. Huge IFE screen, if that's your thing. I'd rate the cabin service above BA, and well ahead of Qantas.
Anyway, given your routing, I think your best bet is BA or Qantas on the way out (QF if you'd like to try the A380), and Cathay on the way back. You should be able to do this all on a BA ticket with codeshare flights on QF and CX, but even if you can't, they are all oneworld carriers and your miles will be credited.