No JFK-LHR redeye because if the flight departed JFK just before the night jet ban started it would arrive at LHR just before the night jet ban ended at LHR. Timings too tight and impractical. Far more comfy to do the Eaastbound in First/Club where you get a decent night's sleep.
People did do the Concorde Cannonball - leave LHR at 1030, get to JFK at 0920. Do the business. Leave JFK at 1325 arrive LHR at 2225 (ish).