> 3. The likelihood of a British constitution is increasing, which would somewhat bind future parliaments.
As an repetition of and an aside to all those pointing out that there is a constitution, what may find gaining some momentum after this are calls for a Bill of Rights, something England used to have[1].
That's a sophist's argument. There's a reason it's qualified as the 1689 Bill of Rights, because it doesn't exist as a bill of rights any more. Parts of it were subsumed by other laws, parts of it repealed - where is your right to bear arms?