All kinds of plausible reasons, Steve, as there are for most mistakes. But for all that, it turned out to be a bad misjudgement. Didn't do anything to stop UKIP. At the very least they could have made support for the referendum dependant on some sensible ground rules.

There was a petition that got a few million votes at the time, calling for a guarantee of a second vote to be triggered if the winning sides margin was less than 5% and the turnout less than 75%. It was started by a Leave supporter before the referendum (who expected to lose) but was signed by millions of Remainers as well as Leavers. That would have been a very sensible requirement.

And the example of the Scottish referendum should have been followed - that achieved a turnout of over 80%, with voting open to everyone of 16 up, including migrants from the EU - the people who stood to be most affected by the result in 2016, along with logterm British expats in Europe, who were also denied a vote.