Depends on your dates and starting point.
I wouldn’t always assume that an ex-EU is always cheaper than an ex-U.K. plus you have the costs of positioning flights too.
BA sale is currently on and ends in a couple of days but they don’t fly there so would be connecting in eg SYD or HKG. And some of their sale fares don’t apply to partners flights.
Cathay via HKG is an option or Singapore via well Singapore and that’s before you start looking going the ‘wrong’ way round and UA via LAx and SFO or Air Canada via YVR
I’d start by looking at google flights and investigating from there.
Huzzah for International Jet-setting !