Just as a quick update and an example for future reference (though this is definitely YMMV territory). I spoke to the IFM on the JFK-LHR leg and she sent a Teams message to the ground with our baggage receipt numbers and they said they could return the bags if we went to the customer service desk. We went to the T5 desk in baggage claim, the helpful lady there spoke to someone else who said we’d have to go to T3 as our connecting flight the next day goes from there. That actually was ideal as we needed to go to T3 anyway as that’s where our car was parked, and it saved us lugging the bags on the train. At T3 we used the phone by Excess Baggage to speak to BA, and yet another helpful person came to get me and take me back airside through the Secret Heathrow Back Passage. He waited with me by the belt and the bags turned up within about ten minutes.

This may well be an exceptionally good result and more than a little lucky, but we had our bags back in just over an hour from leaving the plane. Excellent work from all concerned and I’ll be putting in some very good feedback on the website!