I expect that you will have to write shoreditch_tom. And I would suggest first writing to request a refund explaining what you have said above rather than writing to actually complain. Only if you make no progress from the first attempt would I write a complaint.

For an example of a successful letter to BA see my thread Please constructively comment on my letter to BA claiming out of pocket expenses.

It took about a month from sending the letter to receiving the refund.