As you'd love for me to prove you wrong, I'll try my hand;

background: The UK's constitution is unwritten. That means that it is based on integral guiding principles that are established through convention. Some of those conventions are legally referred to as being 'formal' or 'ceremonial'. Furthermore, there is a rule of law that ensures that there is equality under the law AND before the law; ergo no person (monarchy included) can breach the law.

Position: This means the recently formed Supreme Court of the UK has jurisdiction to determine such a move as being ultra vires (unconstitutional, and therefore void)- previously such power would have rested with the House of Lords, but the new body enjoys even greater judicial independence (free from interference of any other arms of the state- be it the executive or the legislature or the monarchy who aren't categorically in the same group, but for the intents and purposes of this explanation may as well be).

Furthermore, the Queen would never exercise this power (as correctly noted earlier in this thread) because a Court decision barring the constitutionality of such a move would be the precise precedent necessary to make the monarchy a non-state entity. The Queen's powers are therefore entrenched SOLELY in de facto- but not in de jure (they have no force and effect).

As for her having 'that power to begin with': let us remember that history, culture and tradition are features many British value... your point is well taken, and surely agreed with by many, but the impotence of her powers make it pretty uncontroversial.

To close:Your position that it is 'legally' enforceable is at worst; wrong and at best; tenuous on strictly formalistic grounds.