In the UK the police and military swear allegiance to the Monarch. So I think the true answer to this is that it really depends where loyalties lie.

In the US you have the second amendment to protect you against the state, but in the UK we have the Monarch. In theory the Monarch could tell the government to get lost, but their ability to do that in practise would depend on whether the police and military would side with them.

If Charles withheld consent for this he would probably be overruled in one way or another, but if it was about entering an unpopular war you could see how his consent would become much more important.