The version of the story that says that most people actually would be fine with a lot more immigration than we currently have: that most people would see their fears turn out to be unfounded when they saw the reality of what it would actually mean ... In fact maybe they'd be fascinated and delighted to observe the evolution of new creoles and so on. And that mostly the fears they do have are only really there because they have been manufactured by the establishment, those in power and the media they can control.
In that version of things, why exactly is it in the interests of those in power to boil up anti immigration sentiment? They aren't going to live in the types of areas that would see the most change. We know that immigration provides cheap labour, shores up the youthful part of the population, all this positive economic stuff that's in the interests of those running capitalist endeavours.
Why do they encourage rather than supress fears amongst the general population?
I don't really buy it as an explanation. I suspect the truth is that a lot of people do indeed have a fear of change and an instinct to be wary about cultures they aren't familiar with. Whatever their class or indeed whatever their nationality or ethnicity.
I think this matters because it has implications for the best strategy for persuading people that immigration is not something to fear.
bimble says above about telling people they are "asking the wrong question" which is a terrible way to win someone round. Similarly, simply telling them that their fears have been whipped up by a manipulative media, with the implication that they are too stupid to see through it.
Also, if you accept that there are things that worry people, and if you can accept that without writing them off as despicable racists, then you can start to talk about mitigations to allay those worries. They might involve some slightly uncomfortable compromises. Just for example, the kinds of rules that are about what language people should be expected to speak in certain situations, or used on shop signs. I know this starts getting towards French style things about headcoverings or whatever, but it can become difficult even to have a conversation about what might work.