The military swear loyalty to the crown, not to the government. If, perish the thought, the public elected an incompetent malingering buffoon into the office of Prime Minister [cough], who then ordered the military to do something batshit crazy, the officers could ask the Queen (or whoever is monarch if she ever gives up) for confirmation. If she declined to confirm the orders, then the military had grounds to disregard the orders of the government.

Of course, this assumes that the monarch is sane. The Queen, obviously, no problem. Charles - not so sure. His traumised children (well, the one that is still a member of the family) probably, maybe, but who knows what horrors lurk?

So there is the reverse scenario, where Mad King William orders the military to kill all journalists, and the government has to find a way to stop the military from doing that without breaking their oath to the crown.