If your journey includes connecting flights with more than one airline, the checked baggage policy of the airline that operates the longer leg will apply. For example, if you fly with American Airlines from New York to London and connect onto British Airways to Amsterdam, the leg with American Airlines is longer and their baggage policy applies to the whole journey.

See the BA checked baggage page: http://www.britishairways.com/en-gb/...age-allowances

EDIT: With a stopover then the CX allowance would apply for that segment. If you are coming back without a stopover MEL-HKG-LHR then BA's allowance will apply for those segments as per the above.