In the American context, this is really just the distinction between what is in the constitution and what is just Congressional law (is that a phrase?). That's why I was picking up on you saying that judges have a 'right'. Their position isn't necessarily as permanent as it appears, because of how much leeway Congress has to act if they so choose. Whereas if it was explicitly in the constitution, the process for change is much more challenging.
The UK, pretty much anything can be changed by simple majority, so yes parliament could abolish the monarchy of course, and we have very little protection of our rights from the Government of the day (see the British Bill of Rights), as opposed to having a written constitution with a higher bar for change.
What a BORING argument we're having.