Online check in is now working using this link. No need to log in to your BAEC account, indeed you may want to do this in Incognito mode.
https://www.britishairways.com/trave...g/public/en_gb
It's very slow and flaky, and may time out, but if you go in a second time you may see you have checked-in status. This allows an easy reprint at the airport - or online when things speed up.