Simon Tilford has a postwhere he explores the roots of Brexit in a kind of UK exceptionalism. He argues that "the underlying reason [for the Brexit vote] is the hubris and ignorance of much of the British elite, not just the eurosceptics among it". I want to expand on that. I do not think this ignorance and hubris is confined to the UK's role in the world. It also extends to an attitude to knowledge of all kinds, and I suspect it is possible to date when this began to the revolutionary zeal of the right under Thatcher.
The Thatcher government that gained power in 1979 were going to do away with what they saw as Keynesian nonsense, and run the economy using money supply targets. Treasury civil servants produced a forecast that said their policy would lead to a recession, and this turned out to be what happened. The forecast when it was made was dismissed by the politicians in government as the product of outdated civil service advice reflecting a failed consensus.**
It is of course the prerogative of politicians to reject a consensus, particularly if there is a reasonable minority of experts who think the consensus is wrong. It is what happened next that was the problem. Monetarism was a monumental and predictable failure, but Conservative politicians and their supporters spent considerable effort and resources turning this failure into a triumph of Thatcher over an establishment civil service and academic economists. One example is the letter from 364 economists objecting to a deflationary fiscal policy in the 1981 budget. The right, and in particular the IEA, have successfully cultivated a belief that this letter was wrong when in fact it was right. The recovery (using the term as it should be used) was delayedby over a year by the 1981 budget. More generally the view was that social scientists or civil servants were probably antagonistic to the neoliberal project and could safely be ignored. They were, in Thatcher's words, not one of us. 
The reality was that the Thatcher and later Major governments did subsequently often take note of what experts were saying, but the myth on the right prevailed. Before the Conservatives regained power in 2010, they thought very little of going against the advice of the majority of economists over austerity, although to be fair they were later supported in this by senior civil servants and the governor of the Bank of England. Policy based evidence replaced evidenced based policy. But this was the relatively sane wing of the party, as we discovered during the referendum campaign.
We know the EU referendum campaign largely ignored experts, whether they were economists, lawyers or experts in international relations. What I think surprised many is that the Leavers fantasy was not just a device to obtain votes, but actually reflected what the Brexiteers believed. Since the referendum the government has clung to the fantasy, and ignored or dismissed all the advice it was getting from its civil servants. (In two cases dismissed meantsacking or resignation.) As Steven Bullock says, the EU side are in despair that the UK has yet to work out a realistic position on many issues. Because large parts of the UK public, relying on the right wing press for their news, still believe in the fantasy, some in the main opposition party thinktheir best strategy is to ape their opponents.
As a result, we are in a strange bifurcated world. One part consists of pretty well anyone who knows anything about the economics, politics or legal aspects of Brexit. They realise how hard Brexit will be, know how much damage it could do, and by and large think it will be disastrous for the UK. (Experts tend to recognise and respect knowledge in other areas.) The other part lives in a different world, the world of the media and politicians, where everyone still lives the fantasy.
In this respect, we are no different from what is happening across the Atlantic. Angus Deaton notesthe tragic irony that in the year the great nobel prize winning US economist Ken Arrow dies, the Republican administration is ignoring one of his great achievements, which was to show why a simple market in healthcare will not work. The only 'expert' this Republican administration seems to recognise is Ayn Rand. If it is successful in replacing or sabotaging Obamacare, millions will lose coverage and thousands will die as a result. The experts (such as the CBO) who predict this are accused of inaccuracy by a White House that cannoteven be bothered to check its spelling of 'inaccurately'.
May holding Trump's hand shortly after he became president was indeed symbolic. Those who justify ignoring experts often talkabout them as 'unaccountable elites' who have ulterior motives in giving the advice they do. In reality ignoring expertise means dismissing evidence, ignoring history and experience, and eventually denying straightforward facts. It leads to the politics of barefaced lying, such as asserting that a new trade agreement can be negotiated in little over a year.  This disdain for knowledge is not a prerogative of the right: you can find it on the left among those who say, for example, that all social science is inherently value laden and therefore political. (Ironically often dismissing mainstream economics as a buttress of neoliberalism, the same economics that the right are so keen to discredit.) The difference is that that the knowledge dismissing right have power in the UK and US, and so we are suffering the consequences of their evidence-free politics.
 Sir Keith Joseph tried to abolish the Social Science Research Council.  It seems finally that the government has accepted a reality that was obvious months ago to those who listened to experts.
**Postscript 21/07/17 As Sasha Clarkson reminds me, one of that group now spends his time denying climate change.