I think many Brexiteers do come at this from a position of ignorance. But so do many Remainers, and also many Europeans don't try to put themselves in Britain's shoes and think about it from a perspective other than their own.
As an island race, as a nation that has always been somewhat apart from Europe and which has had to defend its freedom from continental tyrants on several occasions, as a nation that had a large empire and often looked to other parts of the world like Africa, Asia, Oceania and the Americas... we naturally have a different worldview to the Europeans. We have a link to Asia, the Americas, etc by way of our relationship with our daughter democracies like Australia and New Zealand.
I can totally understand that after a 20th century that was awful for large parts of Europe, where they suffered two world wars on their soil and then years of fascism or communism (the former for southern Europe, the latter for eastern Europe).. I can understand that they are much more willing to give up their sovereignty. I can also understand that not being a part of the Anglosphere, they also feel somewhat more insecure about Europe's relative decline in importance and wary of a world where an English-speaking nation (the USA) is predominant. All these are understandable and I applaud them for following their desire to extinguish all forms of nationalism. But in this country we don't have a recent history of jingiostic and murderous dictators. We haven't suffered century after century of occupation and massacres resulting from nationalistic fervour. In this country we didn't have 6 million Jews and other minorities murdered in living memory. So we don't have the same driving mindset as they do to extinguish a mindset, nationalistic though it is, that for us has been associated with freedom and singular/unique identity rather than hatred and mass murder.
Part of the problem is that many Europeans seem so insecure about this whole thing that they we can't just say, "Well, thanks for the good times [in the EU]. We appreciate it, but we have a different path. We truly wish you all the best". Their response is, "How dare you leave. We hate you. You're an idiot and a racist if you want to leave the EU". I don't want to be part of a club that has that kind of attitude.