But then often immigration isn't the problem. It is a solution preying on the fear of people that "outsiders" are harming their opportunities, housing, way of life etc. The real problem is that people are not making living wages and wages are not catching up to cost of living.
As politicians pushing anti-immigration come to power they also realize this problem. They'd rather not solve immigration because then they need to face up to the actual living wage crisis issue. It also helps keeping the immigration talking point open so that it can be used in next election.