Bingo! Tons of availability for LHR > TPE be it on JL or EK followed by CI service from TPE to SYD. For instance, here's a Nov 8th departure out of LHR "connecting" onward to a November 9th service on CI to SYD:
View attachment 310952
View attachment 310953
In case you're wondering $3,335 is the price in New Taiwan Dollars which converts over to $159 AUD.
As you can see above there is JL availability which if you book that means you'll save £365 versus the EK departure. I cannot comment on EK or JL service having flown neither, but would find it surprising if booking EK was warranted over JL. Speaking about saving money, one could further shave another £100 departing ex-CDG. Then again, you have to weigh the cost savings over the inconvenience of getting there.