I always felt it was more of a “big country which was once an empire” problem.
Even my tiny Portugal has some level of “celebrating the greatness of the country” on account of what was done by people there 5 centuries ago (i.e. during the time of the Discoveries) and Britain’s “Glory Days” are closer in time, were even bigger and, maybe more importantly, unlike in my country were that kind of stuff is out of fashion because the Fascists were heavy users of it, there are frequent celebrations of past glories some way or another in British media and there is often a nationalistic slant in the reporting of international news (mainly of Britain being portrayed as more important and listenned to abroad than it actually is if you look at the coverage of the same news in other countries).
It’s understandable when you’ve spent your life seeing international news being reported always with a slant that makes Britain seem important (which it isn’t anymore than other similar-sized countries, and often looks kinda desperatelly trying to ride in the coat-tails of America, the real important ones) and were the Imperial past is constantly remembered (nowadays, mainly with films and TV series), one ends up believing “we’re special” and that was easilly weaponized by the Leave campaign and is still weaponized by the Tories.
Most Brexiter arguments wouldn’t at all be believable for those with a realistic and informed view about Britain’s position in the World, the view of Britain abroad and the balance of power between the rest of the EU and the UK.