Yes, it's in the airport records, but not the passenger records. Moreover in pulling bags from the hold, the usual advice would be "we need 3 bags from Smith/ABC123" rather than looking for a specific baggage reference. The information can be found but I suspect over the telephone they are going to be wary of someone with limited information.

But the bags almost certainly will be recovered since clearly they got to LHR. Unfortunately it seems we still have the staff shortage issue on weekend evenings, which then creates work for other people in BA. In future travels it's a good idea to follow the suggestion sometimes made in this forum to (a) photo the bag contents laid out before packing (b) put a card on top of the contents with phone and email addresses (c) photo the boarding pass - more for missing TPs/Avios (d) photo the baggage slip. Google Photos is less likely to lose things and does put a time, date and location stamp on your image.