The ability to log back in to the British Airways Executive Club via their home page has returned.
However, some functionality is still not restored. This is particularly around the Family Accounts settings:
In addition, my latest flights are still not updated although people are reporting on Facebook that their flights have been updated.
I managed to upgrade a forthcoming flight but the voucher I used has yet to be debited from my account, although that may just be a timing issue.
Is the system back for you?