Looking at Google Flights there are some decent prices from Sweden to Australia. These are are sold by Cathay Pacific which operates all but the London-Stockholm legs which are on British Airways instead.
The cheapest price is for Perth, which comes to £1829 / €2083. Other cities on offer are:
- Brisbane £1846 / €2097
- Melbourne £1842 / €2092
Interestingly I do not see Sydney at similar pricing levels.
If you are particularly selective about the aircraft you fly, Cathay Pacific flies different aircrafts to the different Australian cities mentioned above. With A350 (in the main picture above), A330 and B777 for Perth, Brisbane and Melbourne respectively. All flights between London Heathrow – Hong Kong will be on B777s too.
(Thanks to Head for Points for letting me know about the Etihad part)