Heathrow - Mount Pleasant is 7876 mi, just slightly less than JFK-HKG. I think the only aircraft that has the range in BA's fleet is the 77W, but BA's versions have de-rated engines as they were never ordered for ULH routes.

I presume a 788 could get down there. Getting back is another question, the runway at MPN is only 2590 metres. Compared to LHR at 3900 and 3600 metres. Tricky to uplift a full load from that length runway.