The other question here is whether BA applied all reasonable measures to mitigate the delay. It's one thing to delay a flight overnight - perhaps that was unavoidable (though I'd still place close scrutiny to what actually happened - Sigwx may be able to elaborate on this). But to then not depart until late evening the next day? That suggests they didn't have sufficient standby crew to operate the flight ASAP the next day, which would firmly put the ball back in BA's court.

Either way this is one you'll almost certainly have to challenge with CEDR, but hopefully with a little bit more background information you may be able to make some effective arguments against the flim-flam that BA argues.