Well, I received another carefully penned missive from the BAEC team this morning.

Dear Wilco Roger,

British Airways has become aware of some unauthorised activity in relation to your Executive Club account.

This appears to have been the result of a third party using information obtained elsewhere on the internet, via an automated process, to try to gain access to your Executive Club account.

We understand this was login information relating to a different online service which you may have also used to access your Executive Club account.

...

We have now locked down your online account to protect it from further access. As part of the lock-down process we have also changed your password and you will need to reset it before you are able to use your account.
etc, etc

The commonly used abbrevation "W.T.F." is in place here... Maybe the e-mail they sent out by pigeons last Friday finally arrived to our mail server now.

And the account seems to work as it should (touch wood)