You may well see a full redemption refund breakdown if you do it online, and in that situation the Avios comes back within a few hours, maybe 24 hours maximum, and the cash is more an artefact of your bank's refund processes, but with Amex, one of the slickest in the business, it may be 3 days. If you do not see a breakdown then it will go to the back office team and it could take a week or two. You see this breakdown before the final commit stage so you can pull out if you don't see a precise Avios and precise cash amount on screen after the Consent screen. If you need the Avios for the new booking you best call BAEC, and you must call if you don't see a breakdown on the screen.