I think you will find BOAC flew LHR to Detroit back then -car industry-. AF would have probably flown to the French Caribbean but Jamaica very unlikely. Even in Early 70s the Caribbean was a stretch for the then new 707-300s and VC10a and offloading pax or baggage due to headwinds not uncommon.
UK to Caribbean was either JFK and change to the JFK to Jamaica add on leg , not everyday or JFK to Barbados and Trinidad and Bermuda (not in the Caribbean of course ) . Some nice lay overs for the VC 10 crews who operated the trips south of JFK or who crew changed in BDA before the aircraft went further south. More relaxed way of travelling back then at least in terms of journey time .