IDB = Involuntary Denied Boarding (in essence, where you were denied travel because of an action by the airline, in this case their failure to issue the ticket).

You have a strong case for IDB, and for a flight of this length, the legislation says you are entitled to £220 compensation per passenger as a consequence.

If you have not made a claim against BA for IDB, you should now do so. They may pay up, or they may refuse to do so. In the latter case, you then ask BA for confirmation that is their final position (sometimes called a "deadlock letter") and once you have that, you can proceed to CEDR. Dispute Resolution, Conflict Management & Mediation Services - CEDR

CEDR - as the name suggests - is a dispute resolution service that BA has agreed to be bound by. If you and BA cannot agree, CEDR will look at your case and rule on who is correct. BA must abide by the outcome.