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It's not the taxes so much as the fuel surcharge. You can do a dummy cash booking at matrix.itasoftware.com, and see for yourself what the fuel surcharge is.
A one-way from LHR-NYC on BA will be more expensive, because of the UK APD and passenger service charge. It's generally best to fly into the UK, but back from some other European country to avoid the UK APD.
A cheaper way to get from NYC to London using BA miles is to redeem for travel on Aer Lingus JFK-DUB/SNN-LON. Fees will be lower, but EI offers Business Class only on the TATL segments; the intra-European flights are one-class Coach.