When LGW were having their staff shortages with the luggage handlers a year ago they were telling passengers not to wait - go home and we'll get the bags to you by courier. This problem has largely been solved, though 30 minute waits are still happening.

There is a particular problem with EDI baggage return, it's in a public area so I'm not sure I would want to leave it to chance, or indeed the light fingered. But my hunch is that they would take the bags off the carousels and by next morning they would at some point think about shipping them off to their owners. So if the OP rolled up then you would probably be allowed to take the bags away with you, I doubt they would have got very far with processing them.

In theory you should fill in the customs form BOR1422 if the baggage is off an international flight outwith the EU. It's online:
https://www.gov.uk/government/upload...yedBaggage.pdf