It's a poor show from BA.
Case example - QF in Sydney back in 2009. One of their (then) new A380s went tech prior to boarding the SYD-SIN-LHR flight, and I couldn't wait 6hrs for the inbound A380 to arrive, be turned and readied as I had to get back for a funeral. So, after a short while of ('not possible'), QF made it happen - they handed me the phone to the guy going through the bags and asked me to provide a 'visual' identification of the bag in addition to the tag number.
24hrs later, bag is on the belt waiting for me as I arrived on my rereouted journey on board SYD-BKK-LHR.
It is possible - if the airline is willing to pull their finger out to make it happen