It's kind of ironic, because a massive reason for the enshittification of Twitter is Musk's rampant transphobia, and the BBC is famous among the trans community for platforming transphobes. I'd have thought they'd be perfectly happy to stay on Twitter.
I mean, there's a lot more wrong with Twitter than just transphobia, but you can trace it back there. It was a big part of the "free speech" argument that transphobes were getting silenced, which is what drove Musk to want to own the site, and also drove him down the right-wing-identity-politics rabbit hole that turned him into the wingnut he is today. That and anti-COVID measures hurting his bottom line.