Bungling the split up a union is far better than ignoring the will of your constituents.
That's especially true when equally non-binding but current polling of your constituents on the same question shows that the opposite side quite likely leads now that the concrete options are known.
It's a well-established British Constitutional principal that a Parliament cannot bind a future Parliament. Why would one view the public will ant differently, even if it were fully informed?
Representative democracy means that they determine policy by choosing representatives. It's disingenuous for those representatives to turn around and blame their own policy choices on an explicitly non-binding referendum that they sent to the public. (Especially so for a leader of the party who choose to do that specifically as a means of minimizing the impact of the issue so referred on a general election so as to preserve their partisan majority.
Then it should have been a binding referendum.