Just not sure what company or anything!

Ideally we want a ticket that goes

UK to Sydney (start journey)

Syd to Melbourne (a few weeks into journey)

Melbourne to the UK (end of journey)

Lot's of flights by different carriers go Europe - Asia - Sydney -
Melbourne - Asia - Europe. So get on of theses tickets Europe -
Melbourne and stop over in Sydney for a while. And when you are not sure
about the carrier take one of the asian (Singapoore, Malaysian or Emirates)

Niels