The cause — or causes — for the account compromises is currently unknown at this time.
This is the latest in a disturbing string of breaches of frequent travel loyalty program accounts where miles or points have been used; and information of the account holder has been changed without authorization.
My advice to you based on my experience is to not panic; but do contact a representative of the British Airways Executive Club as soon as possible and give them as many details of the breach of your account as possible. You may not be able to get through immediately due to extremely high volume at this time. Get records of the most recent balance of Avios you had in your account, just in case you may need it.
At worst, this should be nothing more than a moderate inconvenience to you. You will not lose your Avios; but do not expect for them to be restored to your account immediately.