There's no doubt that Leave the EU (Brexit) was fueled by anti-immigration sentiment in the UK, and that the Brexit victory was carried by white labor voters in the UK. Further, Trump has indeed built his campaign on the same kind of anti-immigration views, and white Americans, especially men, are among his biggest demographics.
But there's a crucial difference between the demographics of the UK and the US. In the UK, the white vote comprises about 85% of the voting population; in the US, the white vote is closer to 70%. Further, the non-white vote in the US - in particular, African-American and Latino - are strongly anti-Trump.
That minority has already served Hillary Clinton very well, bringing her landslide victories in the US South, and an impressive victory in California. There is no reason to think that even a sliver of that vote will go to Trump in the Fall.
In addition, Hillary does far better with white women in the US than Brexit did with white women in the UK.
We still have a very long way to go until our election in November, and the forces of progress need every vote we can get. But there's every reason to think that Trump and his pandering xenophobia will not have the same result his spiritual brethren got with it in the Brexit victory last night.