Lawyerboy - I used to use BA and SQ out of South Africa, generally going as follows: CPT - LHR - ZRH - LHR - FRA - LHR- EDI - LHR - JFK - SIN - SUB - SIN - BKK - MRU - JNB - CPT.
The LHR-JFK sector is on Concorde; and all other sectors except the European ones are in First Class. That little lot costs US$5,000 which is an exceptional deal as far as I am concerned!
Out of interest, why are you flying eastbound? Constant jetlag will be the order of the day!!
Be advised that Lan Chile looks like it may well be on strike.