As you say, I think it is very clear that the Astronomer Royal has a conflict of interest as the Chair of the STFC panel which took this decision. Plenty of professional astronomers feel the same way.
What more evidence is needed, than the way the Astronomer Royal for Scotland has been doing all the media interviews in defence of Jodrell, while the Astronomer Royal for England has stayed quiet? Last time I checked, Cheshire was in England.
I doubt that the BAA holds much sway on this issue, or that His Majesty has much inclination to intervene. But publicly drawing attention to the conflict of interest, and the way England’s Astronomer Royal is currently AWOL, can’t do any harm.