That is not true.
The leaders of both the Brexit campaigns (Boris Johnson and Nigel Farage) both clearly said that they wanted more non EU (so mostly non-white) immigration - provided it was skilled people. Government policy since Brexit has made non-EU immigration easier.
Remainers wanted less non-EU immgration and more EU immigration.
So somehow the people who wanted less white immigration and more non-white immigration are the racists?
This is one reason a lot of us Brown people voted for Brexit. not my main reason, which was mostly opposition to further integration (the commitment to "ever closer integration") and some aspects of EU decision making, legislation and regulation.