You need to find out from BA if the Agent has paid for the ticket or not.
If the Agent has paid for the ticket your'e golden - if not then you're in trouble. If the ticket is not paid for it depends on if you paid for it with a credit card or not, whether it has ATOL or not. First line of defense is ATOL if not you will need to rely on Section 75 if you paid on a CC as the CC is jointly liable.
I had a similar issue that the agent I booked for a CX ticket when bust but thankfully they had paid up so I was able to fly.