I would have routed ORD-MIA-LAX-LHR or via one of the other west coast cities (SFO, SEA, YVR) instead of ORD-LAX-JFK-LHR. The longer flight to LHR from the west coast makes a huge difference in the amount of sleep you get. But by going BA from JFK you do get to have dinner in the Concorde room (now the BA dining room) and use the sleeper service on board which does make it a bit more tolerable (just barely, winds were good last week so JFK-LHR is well under 7 hours).