MOnica That is true in some Labour areas, which voted Brexit, but not in all, by any means. For example, Hartlepool has a very low number of immigrants and the percentage of immigrants in Stoke is below the national average. On the other hand, London and Manchester have a high percentage, as does Cambridge. Areas which have suffered economically tended to vote Leave, whereas those which have prospered voted Remain, regardless of immigration. It's probable that immigration became a scapegoat for people's anger. There's also the issue of culture. Areas with high numbers of elderly people also tended to vote Leave, regardless of the number of immigrants who lived in their areas.
The ridiculous thing about immigration is that the number of immigrants from non-EU countries is higher than from EU countries and always has been. There was no reason at all why that couldn't have been curbed, because the UK has full control over immigration from non-EU countries.
There was a vox pop interview with somebody before the referendum. A man was asked why he was voting 'out' and he stated that it was so all the Muslims would be sent home. Brick wall anyone?