I'm ignorant of many of the specifics, so I'll try not to embarrass myself, but as an outside observer, it seems like the Leave voters DO view the UK as special, and as well they should. Your history is one of going it alone (until you ring us) , and of succeeding as a people by not attaching yourselves to a foreign bureaucracy.
But I can envision the the UK fracturing, with Scotland voting themselves out of the union, and Wales thinking about doing the same, although unlikely. NI will stay in the UK, but if this goes through, Scotland will set another vote, and they'll vote to stay in the EU, effectively severing ties with the rest of the UK.
But again, I really don't know WTF I'm talking about, so Mission Embarrassment accomplished!