Does OP has a choice of scheduling? Is this a personal or business trip?

I know many people have Sunday meeting at the office and fly out BA CW overnight then go directly from LHR to London office for meetings.

If I were do this this schedule, I would go for a 2 hour massage at my favorite spa, have the car pick my up directly from the spa to JFK, take a shower at the lounge, have the pre flight dinner and a few glass of champagne. I will definitely get a good night sleep on the plane and be refresh the next day.