There's a night curfew at LHR, so that's out of the question.
Instead, it would be good if BA added a flight that leaves LHR at 2100 becomes BA 180 the following morning. And instead, turns BA181 around immediately with a late night departure from JFK around 2340.
Air Canada used to run flights LHR-YYZ on that schedule but stopped. Not sure why as I thought it was always rammed at the pointy end (yet empty down the back).