"Listening to people's concerns" does not mean purely "make immigration rules even stricter than they are now." They're already so strict they're actually causing illegal immigration at the same time as damaging higher education and healthcare by making the UK less attractive to work in - for people born here as well as people moving here.
It could mean taking into account that asylum seeker map and allocating more resources to areas that take in more asylum seekers. Resources in terms of jobs on the ground, bus routes. English classes, school places, extra GPs or extra funding for GPs (GPs get paid the same per patient, which benefits only those in richer areas), more building of new homes for social rent, more funding for things like community centres and libraries.
Planning for accommodating people moving to the UK (for whatever reason) rather than either trying to stop them coming or pretending that the change in the make-up of a local area makes no difference. Or pretending that someone immigrating to the UK now is in the same position as white people with white British backgrounds because "we're all descended from immigrants."
All practical stuff which has suffered in ways that are completely unrelated to refugees and other immigrants, so needs better funding and organisation anyway, but if one way to get them done is to say they're to deal with the effects of immigration on local communities, then that's a tactic to take.
Social housing is sometimes allocated to settled asylum seekers ahead of people born in the UK (because they're in desperate need), and that pisses off the UK people on the waiting list - and trust me, I've heard that from plenty of people who are not white. The solution is not to shove new residents further down the list, it's to make the list bigger by building and acquiring more homes. That's just one example.
And some of that helps with the cultural aspect, too. There is some resource-based reasoning behind the recent upsurge in racism, and it feeds back into cultural concerns that are much more difficult to tackle, especially since a lot of it just takes time. Generations (or at least a generation), not months or a few parliamentary terms.