Nonsense. They voted Brexit in the main as a protest.
Take South Wales. Are you seriously telling me that huge swathes of immigrants have had an effect on wages? Really? Absolute bollocks. It's interesting that immigration is seen as a problem in Wales, yet it's a part of Britain that has been far less affected by immigration than most other areas (historically Wales is mostly made up of immigration, but that's another story). The parts of Wales that voted Brexit most strongly are the areas that have had the lowest amounts of immigration.
Too many people swallowed the bullshit the media gave them. Too many people have been swayed by the blame immigrants tale, in the same way that they are swayed by the benefit scrounger tale. It's called divide and conquer. Blame those in society that can't fight back.
Brexit is a sham. It won't make any difference to the type of immigration people don't want (only the UK government can do that). It won't make any difference to wages, until we fail to get trade deals and we're living in UK PLC sweat shop and wages go down.