I believe the US carriers CoCs do reference downgrades, and note that you will be given an "appropriate refund" (AA's language). If it's not in BA's CoC, and you argue that the downgrade was a breach of contract, I doubt you could claim damages for more than the fare difference (though would love to see someone go after them for pain and suffering). But the EC261 downgrade comp is invariably a larger amount.

It really, really, sucks to be downgraded, and I'd be really, really pissed, but perhaps some perspective is warranted as there are larger problems in the world. Take the compensation and move on, and perhaps that means never spending another dime/shilling on the offending airline again.