If it was done online via BA.com then usually the cash is refunded within 2 or 3 days. It's nearly immediate at the BA end, it's more about how the banking system processes the payment. So you can perhaps judge this from other online cancellations you may have had in the past. This is contrast to the manual refund system in BA which is much, much slower. All tickets can be cancelled in full and without charge within 24 hours of purchase, so being flexible made no difference in this instance.

Welcome to Flyertalk kt31981, welcome in particular to the BA forum, and I hope that we will see more of you in the future.