Originally Posted by
antichef
If you are denied entry, then you will have to stay airside. Then unless you have lounge access you will have only the enjoyment of LHR shopping and airport food for your layover.
Ah, but this is the real problem. You can't stay airside overnight at Heathrow, hence my suggestion of trying to get a same-day connection.
Alternatively, can the OP get somewhere near Boston (NYC, maybe) with a same day connection or avoiding London?
Heck this might be overstating the entire situation, but it's not a risk I'd want to take myself.