Okay, well you did say income inequality. Even in terms of regional inequality the UK is still very average. Almost all countries have geographic economic divides (West Germany vs East Germany, Sun Belt vs Rust Belt, Wallonia vs Flanders etc).
Most of the 48% accept the result and just want to get on with Brexit. Parties that supported the Brexit result got c.90% of the vote at the last general election. If there was some kind of 'culture war' backlash then why didn't the Lib Dems/Greens/SNP do better than they did?
The difficulty with grandfathering is uncertainty over future UK-EU trading arrangements, since much of it hinges on that. Sure some already completed have been done with irrelevant countries, but others (USA, Aus, NZ, Swiss) are our biggest partners after the EU27.