The reason there was a referendum was largely because those opposed to EU membership managed to persuade the government to let the people express their view. I think that's a good idea when you are talking about major constitutional issues but it wasn't required.
The principle of Parliamentary sovereignty states that Parliament cannot be bound to any action by any outside force - so a referendum could not be formally binding. But other basic principles apply as well - once the will of the people has been expressed, Parliament ignores it at its peril. Functionally, Parliament can be expected to give effect to the will of the people on this - but cannot be forced to. It's a fine distinction but it matters.
I expect what will happen now is that when a vote is called, both the Conservative Party and the Labour Party will issue a whip to their Members telling them that they are expected to vote 'Aye' to Brexit and that any Member who goes against party policy can face disendorsement at the next election, or even potential expulsion from the party. They may allow their MPs to abstain without consequence, so nobody will be forced to vote for Brexit, but the vote would pass the House on the Ayes versus a lot of abstentions. A minority of MPs may rebel and vote No, but not enough to put the vote in doubt.
Very interesting. Thanks.