Note: if you have enabled the Cache BB Code Output setting in the AdminCP > Options > Performance page, then all of your posts will be cached in the xf_bb_code_parse_cache table, so you won't see the changes applied immediately after running Andy's query above.
To refresh the cache, simply run the following query when you are done:
TRUNCATE TABLE xf_bb_code_parse_cache;
Like dethfire, I also just moved from HTTP to HTTPS and updated all the internal links in my forum. I couldn't see the changes, but this was why. Hope it helps someone else.