Leave T3 at LHR. The BKK and SIN/SYD services only operate from there because of the JBA, thus retraction to T5 almost certain.
Restart operating to MEL. The "tagless" BKK service could easily extend to MEL as a stopgap whilst future plans are sorted.
Restart AKL. Your choice - over LAX or maybe KUL?
Order the B747-8i to operate Far east services that the A380 is too big for. (And 787 too small)
BKK/SIN may move to T5, but there's not a chance of BA restarting MEL. It was pulled because of poor performance years ago. AKL is already covered via a codeshare with Cathay Pacific from HKG.
It's not clear yet whether BA codeshares with Qantas from SIN will remain. Though as Qantas has said these services are to be retimed, the connections may not be competitive.