Get the consulate to print your whole itinerary on the ETD. If you’re overnighting in London, and border force tries to retain them, ask them if you can keep them to complete your travel. If they say no, head straight to the London passport office and pay the extra to get a 1hr replacement passport, then head to Heathrow as planned the next morning.

Edit: Ah, yes, it’s 4hrs and you need your old passport to do this. Sorry!