Quicker to fill out a small claims court claim form. Send a copy to the BA legal team confirming you will be making a claim in the next 72 hours.
You can judge the strength of your case by the time it takes BA to respond…
Can’t argue with that approach. Haven’t done one of those in years. Understand there is a fee of around 60 pounds if you file it though. Still, it’s guaranteed to get BA’s attention and, as Martyn suggests, you’ll get a taste of how seriously they’re taking your claim.
Best of luck.