@gemlog Maybe, maybe not. Could be the BBC has a long-standing policy that Mr. Lineker infringed — I'd disagree with that policy if so. I don't know enough about how this decision was made or of similar cases in the past to have an informed opinion.
I'd bet that Downing Street did not phone up someone at the BBC to complain, and also I'm confident the BBC bureaucracy is not principally composed of Tories, but it is possible poltical appointees in the BBC made this happen.