This process of withdrawal into the relative safety of internally cohesive groups and group identities is intrinsically messy in globalized, multicultural societies.
A great many narratives are drifting around the Brexit pool: a return to sovereignty, class war, "controlled demolition," nothing-but-another-political-Kabuki- spectacle, end of the European Union, etc.
I think it boils down to something much simpler: the pie is shrinking, and the illusion that it's about to start growing has been shattered. For many communities in the developed world, the pie started shrinking in the 1970s, and has been shrinking (despite the narrative of "45 years of strong growth") since then.
Labor's share of the GDP has been declining for 45 years. Occasional blips higher during debt-fueled bubbles quickly fade when the bubble du jour pops, and the decline of labor's share of the economy resumes its trendline decline.
Since 2008, the only group who feels the pie is growing is the class that has benefited from the unparalleled expansion of debt and leverage, financialization, globalization and central planning--roughly 20% of the work force, with the top 5% gathering most of the gains in income and wealth, and the top .1% gathering most of the increase in wealth. (See chart below)
For seven long years, the citizenry has been told the economy is expanding and therefore they're "doing better." But this narrative is not supported by their actual lived experience. Inflation is woefully under-reported by official statistics, and the rosy "rising employment" narrative is based largely on part-time jobs in hospitality and food services (bartenders, waiters, etc.) that are highly contingent on the spending of the top 10%.
While supporters of the status quo are quick to deride supporters of Brexit, the cold reality is the economic pie is shrinking, and Brexit is a direct result of that reality.
A shrinking economic pie generates widespread insecurity that pressures every status quo arrangement as people circle the wagons in an attempt to protect their remaining slice of the pie from others' claims for a larger piece of the dwindling pie.
The general media line is that the Brexit vote arose out of anger with the status quo's inequalities and asymmetries of wealth and power. While this is largely self-evident, it isn't the most fundamental dynamic at work. I see Brexit as a reflection of our naturally-selected defensive response to insecurity and instability: circle the wagons.
By circle the wagons, I mean our tendency to withdraw into an internally cohesive group with defined membership and boundaries.
The largest such political group is the nation-state, and so it is natural for people with strong national identities to circle the wagons around their national identity.
We can also expect people to circle the wagons around ethnic, religious, localized and economic-social class identities. (Some people might feel more kinship with other fans of Manchester United than they do with any religion, ethnicity or state.)
As people identify themselves as members of the class that has not benefited from neoliberal/globalized crony capitalism, the ruling Elites become the "other," i.e. "foreigners" with whom we have little contact, people who "aren't like us"-- in effect, an "enemy class" that is inherently opposed to our self-interests.
This process of withdrawal into the relative safety of internally cohesive groups and group identities is intrinsically messy in globalized, multicultural societies. No wonder populations are dividing into camps of increasingly angry people with little interest in compromise. Our instinct is to seek clear delineations of "us" and "them" and to seek the relative comfort of "us," which in a multicultural nation, can contain quite a mixed bag of people who nonetheless feel a shared identity.
Much to the chagrin of political parties whose success is based solely on "identity politics," the emerging group identities are not conforming to the political classes' conventional fault lines. "Us" for many people includes everyone who isn't a protected insider of the status quo, and "the enemy" is any protected insider of the status quo.
That includes virtually the entire political class, the entire class of state nomenklatura/technocrats, the entire banking sector and the wealthy class that's benefited so handsomely from the globalized, debt-leverage bubbles and state / central bank support that characterize this era of neoliberal/globalized crony capitalism. 
Nothing to see here--move along, folks--you're better off than ever before.
