It's not quite as simple as that. Much of the country is prosperous but still voted leave, many working class people live in cities and voted remain, and it's quite hard to define working class now in a country which gets ~10% of its GDP from industry and most of it from services.

There's stronger signs of a generational split, and a rural/city split than a simple rich poor split and of course each area has substantial numbers of voters who think differently. Lots of rich people voted for Brexit, lots of people who are not nationalists voted for Brexit lots of people who are not particularly racist voted for Brexit, etc. The reasons are varied. I disagree with Brexit and think it will end in disaster (esp. for labour as you point out), but the view above is unduly reductive.

Unfortunately such a nuanced reality doesn't fit into a sound bite and people prefer to neatly put their opponents in a reductive box, so here we are talking about cities vs countryside and rich vs poor.