I agree; most other countries that use referendums would require some form of minimum threshold (or even a supermajority of, say, 60, 65 or 66% either of votes cast or of the total electorate) for any kind of constitutional change, and certainly for a radical change that would fundamentally alter the country's constitutional settlement and societal norms.Except only 37% of adult British citizens actually voted for Brexit, given a number of people did not vote. You don't make radical changes based on what 37% of people wanted on a random day in June 2016, though I will say that was Cameron's fault in designing the referendum in such a simple-minded way. Also, EU citizens, who are most effected by Brexit, were denied the vote which in my view makes the whole referendum invalid. Radical changes to the UK's relationship with its neighbours should require a very substantial majority, not 13 for vs 12 against which is basically a tie. The Scottish independence referendum was designed in a much more intelligent way because it did require a substantial majority to pass.
And even if you do accept that Brexit must happen because 37% of adult British citizens wanted it, the referendum did not actually ask people whether they wanted to stop EU citizens emigrating here. This was purely something the Tories - May and Johnson - decided to do unilaterally afterwards. Many of us resent this deeply - the Conservative Party have not only taken away EU citizens' right to live here, they have taken away our automatic right to live in EU countries, a right we have had for around 30 years.
Exactly, that, together with the substantially less-than-100% turnout (only 37% actually voted for Brexit) and the denial of the vote to EU citizens, who are the ones most affected by it, means that I have never accepted the actions performed by the Tories following the result. And that's before we start questioning some of the blatant lies ('EU citizens' rights will not be affected' - if that's the case why did they require 'settled status') of the Leave campaign.
Public opinion is liable to change as circumstances change, so a minimum threshold ensures that there is clear evidence of a strong and permanent consensus in favour of the proposed change before implementing it. If there is a minimum threshold, it is assumed that eligible voters who don't vote are happy with the status quo.
Mind you, there is also a school of thought that says that for a referendum to be unbiased, and so that nobody's vote is worth any more or any less than anyone else's, both the status quo and the change that's being offered need to be allowed a level playing field; therefore it's only fair that only a simple majority should be required. Opponents of a minimum threshold also argue that such a threshold can be insulting to supporters of the change because it tells them that their votes are worth less than those of supporters of the status quo, that it can lead to feelings of bitterness among supporters of the change if there is a simple majority in favour of the change but the requisite threshold isn't met (as happened in the 1979 Scottish devolution referendum), and that a minimum threshold can be a disincentive to vote if you support the status quo.
Those arguments do have some merit, but IMO on balance it's more important to ensure that there is a strong consensus in favour of a major constitutional change before implementing it. If you only require a simple majority and the result is close, it shows that the country is bitterly divided on the issue. Besides, even if there's no minimum threshold, complacently believing that a win for the status quo is in the bag can also be a disincentive to vote. People are psychologically more inclined to bother to vote for a change that they positively support or against something that they dislike than for a status quo that they're happy with. A minimum threshold also provides a safeguard against people using a referendum to cast a protest vote or voting for the opposite of what they really want in the hope of getting a close result.
I seem to recall that John Major toyed with the idea of putting the Maastricht Treaty to a referendum (and/or the Tory Eurosceptics tried to put pressure on him to hold one) but he decided against it. This may have been at least partly for fear of losing, but I also suspect that it was because he realised that such a referendum would have risked tearing the country apart. Rightly or wrongly, he believed that avoiding that risk was, on balance, more important than avoiding angering the Eurosceptics within his own party.Why were we not given a referendum on the Maestricht Treaty. I mean one; not keep voting till we get it right. It's what cost John Major his job.