There is a further escalation after this too, so you're not at the end of the road quite yet. As Jerry has suggested, call BAEC, ideally UK afternoon just after lunch time, and be prepared to send in boarding passes if necessary. The information needed is ticket number, PNR, flight number, date, seat number, name.

If this is webforms going to and fro, what you have seen is quite normal, luckily BAEC contact centre staff are well aware of this.