So what on earth were you talking about, keith, when you said, in reference to precisely that point, that "Yes, it is disputed"?

Whatever "pledge" might have been given by the government in advance of the referendum, that can have no legal force. Laws don't work like that.

Even if the government had said "parliament will have no say in this" - which it did nor - that would legally have no effect whatsoever. What determines whether parliament has a say or not - which still has to be determined - is whatever legislation is in force at present, as interpreted by the highest court.