Iain
Do you mean you want to fly from one of the regional airports, as I believe none of the airlines you named fly from Gatwick, all use Heathrow.
I haven't flown with either Qatar or Etihad, I'm not sure if Qatar fly to Oz but they are a highly rated as are Etihad.
I have flown with both Cathay and Singapore, would not fly economy with Cathay as they have very cramped seating, Singapore service is good their seating in economy varies.
I flew to Oz a few years ago in business class with Singapore, very comfortable with excellent service. I have flown long haul business class with BA and found their beds(really flat) more comfortable than Singapore's whose beds slanted somewhat and the service was very good. Business class in lots of airlines is being updated all the time. Malaysia Airlines are excellent, normally good service with good leg room in economy so I imagine their business class would be good, stop over would be in Kuala Lumpur, Thai Airlines in economy are roomy but the entertainment system needs upgrading, their stopover would be in Bangkok.
If you fly Cathay you would have a stopover in Hong Kong. Emirates are also a possibility though I have read lots of reports that their business class doesn't compare with other major airlines. Stopover in Dubai.
I think BA, Singapore Airlines and Qantas use Singapore for their stopover.
check out
http://www.airlinequality.com for reviews on all of the above airlines.