I don't see how Parliament can reverse a referendum result, without going back and asking permission first.
Obviously our constitutional position is that "no Parliament can bind the hands of future Parliaments" - so it's not unconstitutional. But it's politically unaccepable. Also our constitution works by precedent. We joined the EU without a referendum. But after a huge political argument, we had one on whether to stay in or not. So that sort of sets a precedent that the EU is now a decision for public vote. Particularly as we had an agreement from both major parties that we shouldn't join the Euro or sign the European Constitution without a referendum. Although admittedly they simply renamed that the Lisbon Treaty and pushed it through largely unchanged - and it's arguable that this was the breach of faith that massively increased support for leaving the EU and made leaving much more likely. I still don't think it would have happend without the Euro-crisis and a decade of unprecedentedly high net immigration though.
So I'd say we're stuck with referendums on major EU issues now. Our constitution changed by precedent. After all, each time we sign another EU treaty previous Parliaments were binding the hands of future Parliaments in that they were giving away their power to make decisions in major areas of policy to the EU.
There's a good argument that if we do want to stay in the EU we need a written constitution in order to protect us from EU mission-creep.