This comes up fairly regularly. When you cancel online there are 2 possible routes. One route gives the breakdown of refund Avios and cash, and if you see that then it's near immediate. The second route does not do this but sends it off to a back office. That typically takes a month or so. At least in theory a BAEC agent can release the Avios, but if you wanted the Avios immediately in this scenario, and where you did not see the breakdown of cash and Avios, you best call up to cancel rather than agree to the back office process. You will get the Avios and cash, but it may take a number of weeks.

This thread is one of quite a few with more details:
https://www.flyertalk.com/forum/brit...os-refund.html