I don't think parliament should be consulted. We should be able to trust parliament to enact the will of the people, but a huge number of MPs have made it clear they want to ignore them. If parliament is knowingly acting against the will of the people then wouldn't you consider that to be unconstitutional too?
I'm not suggesting the government imposes something because they want it, I'm suggesting they impose something because the electorate wants it.
"If parliament is knowingly acting against the will of the people then wouldn't you consider that to be unconstitutional too?" Undemocratic probably(representative democracy vs direct), unconstitutional probably not.
Again even if I agree with your viewpoint there is nothing to allow it to happen, we would need to change the law of the land. There is nowhere that says that this referendum is binding hence it has to go to parliament, this is what yesterdays judgment means in practice. There is no process for your solution so it is moot.