1. It appealed to misguided "British" values
Millions of Brits were attracted to the idea of homogenous England of old. Xenophobia is on the increase and Brexit did a great job of normalizing racism across Britain.
"There's a little Hitler in all of us", wrote Andrew Sarris in 2002, "if we are not held back by any moral or social restraints."
Brexit made the normally pathological act of denouncing ethnicities and religions a normative one. Much of the campaign rested upon the idea of an imagined Britain of the final years of WWII when Churchill was a hero and Ghandi a terrorist.
2. They weren't wrong about the EU
The EU is a very clunky beast which was caused a huge amount of economic problems for countries such as Greece, Portugal, Spain, and Ireland.
It's a system of open markets in which competition is eviscerated in a shared currency. Britain has never taken on the Euro, and therefore managed a position of reasonable strength - but the Brexit mob isn't wrong about the unwieldly and regulated organ.