I echo the endorsements of AA. As noted AA has an excellent schedule LHR-JFK, and the Y-class service is very good. I have also found LHR staff to be very friendly and helpful, particularly towards AA elites (of any level). AA also has good options LON-ORD/DFW/LAX and beyond, should other US destinations become relevant. AA also has a reasonable network between NYC and LON via gateways, such that one can fly LGA/JFK-BOS-LHR if for example the lowest fare classes on the non-stops are sold out or construct an open jaw for LHR-JFK/BOS-LHR. I have even recently seen LHR-JFK-CDG-LHR routings (BA code-share CDG-LHR). While not necessarily optimal, this flexibility could be useful in relation to other travel plans and when low fare classes are sold out on non-stop flights.