The BBC reported that a number of people appear to have their air miles accounts cleared out, or even used to book items using air miles.
But BA said only a small number of people appear to have hit – and it has written to all its users to notify them of the problem.
The report points to Flyertalk.com, which has several people complaining that the BA points – called Avios and two rooms in Spain were booked under the name of the person who owns the account.
Some people, apparently, had their own mobile phone number substituted for a Russian number.
BA said that its customers could be re-assured that their personal credit card details hadn’t been hacked, and it has taken steps to prevent the hack from happening again.