Trilarion: That happens if you do not have a written constitution and decide to ask the people in an officially non-binding referendum. Then it can happen that voting doesn't really matter, although, if parliament decides... these people were elected too. What you probably mean is that direct singular voting is challenged because the legal terms of the referendum were so unclear. All these questions now asked, could have been answered already a long time ago. It's a bit unfortunate that they discover this only now.
Anyway it's just the high court, let's see what the supreme court has to say about it. And even then it's not sure the parliament will act against the popular vote. I think they would probably just agree, maybe with some demands on how to actually do it.
People voted for Brexit, but let's face it, they didn't know what kind of Brexit they wanted nor what deal they can realistically expect. Did the 350 million pounds each week already materialize? I don't think so and they never will.
A strong Parliament is in principle something I like very much. They should have made the terms of the referendum much clearer right from the beginning.
What I would like most, would be a second referendum right before the end of the negotiations when it's clear what kind of deal can be made. This would be much better direct democracy than this singular referendum where just a small group decided what and when to ask. Maybe a year before or a year later the result would have been the other way around. Not that I don't respect the outcome of the referendum, but one should see the weaknesses of the whole procedure as clear as possible.