The people were given the “ultimate choice”, let me remind you of what that choice was.
“Should the United Kingdom remain a member of the European Union or leave the European Union?”
They were not asked "Do you want the UK to remain in any of the following:
The Customs Union;
The Single Market;
The Common Defence and Security Policy;
They were given the binary choice of remaining or leaving in the European Union, with the government authorised, by virtue of the referendum, to decide upon the implementation of said decision.
There’s no real problem in theory, but first of all, let’s not kid around. You don’t really care whether or not that’s the case, you’re just hoping, for whatever reason, the result would be different the second time around.
In reality, the main issue is that appetite for a second referendum is difficult to measure. Current opinion polls suggest a second referendum is very much undesirable and that the UK should still leave the European Union, therefore, there’s no need for the government to adopt a policy of a referendum on the terms of Brexit.
In the event public opinion turned dramatically, that would be reflected in how the public lobbies MPs, the level of publics support for the government would clearly drop as the government is committed to delivering Brexit, etc. Ultimately, the most ideal situation would, if it appeared a new mandate was required, a general election would be called with parties standing on different platforms on the issue. As I’ve said before, it’s my view that referenda should only be undertaken in very broad decisions, as opposed to the specifics of policy being let to referenda.