Oh, how nice.
We called the number, and got a message saying that their internet support desk is closed for the evening, and that we should call back during regular business hours. Even British Airways' primary reservation line is currently closed, and won't open for another 6 hours.
So, has the ticket been purchased? We're dealing with a flight a little more than a week away, so should we reserve the flight through another airline? Making things worse, this flight was to be the middle flight in a sequence of flights; should we make reservations for the other flights assuming this one goes through, or should we wait?
It would have been nice if the error message could have given us more information so we could have determined these things ourselves. We'll find out tomorrow morning, when the lazy bums decide to start answering their phones.