If as you suggest, this document takes power away from parliament and gives it to ministers, then it is itself illegal and will be repealed with little difficulty, as it is constitutionally insupportable. No need to attack future decisions, just get to the point and pull the rug.

Consider the logic - if parliament passes a bill undermining it's own authority, then it simultaneously undermines the authority of the bill it has passed, rendering it meaningless. That is the constitutional fallacy that the courts will not uphold.

The court does not recognize any higher authority than parliament unless parliament demands it. In this case, parliament does not. The exec can make as much noise as it likes but it will be wasting it's time.

Are you sure you're appealing to the right house of lords?