Perhaps under the idea that this way they'll keep it so?

Almost certainly not.

There's any doubt, much less "almost certainly not", that people who voted for brexit motivated by immigration in areas with fewer immigrants, did it to keep their areas with fewer immigrants?

That's right. There is almost no chance, in my opinion, that people in immigration-light areas voted to withdraw from the EU because they wanted to have fewer immigrants in those areas, simply because there are almost no immigrants in those areas anyway.