I was looking at this earlier.
I don't think most of the suggested responses here are great. They have too much of the "you're asking the wrong question" tone. It's not that I disagree with what is said, it's that I think it should be more targetted at people's immediate concerns.
For example, if someone thinks that lots of tax money is being spent on "immigrants" then a very strong response is to point out that immigrants pay taxes. That's a pretty straighforward way of trying to change what the typical immigrant looks like in someone's mind: someone paying tax rather than having taxes spent on them. Yes you can also go on about tax avoidance, and maybe it's helpful to get people aware of & angry about that, but also it's not something they can actually do anything about in an immediate sense. It's not answering the immediate question or concern.
Likewise with the NHS, pointing out that an immigrant is more likely to treat you than be holding you up in a queue is something quite immediate and direct. It's very likely that this will match with someone's experience when they think about it. They do mention this, but why is it not the first thing in their suggested responses to that point? Make the easy point first then go on to wider politics stuff.
The responses to the first two items simply don't address the concern that is being aired. If someone's genuinely and seriously worried about their job being taken, what does that answer do to reduce their anxieties?
Why isn't the answer to "migrants are all criminals" simply "they aren't"? If you answer that kind of question with handwaving about
how much stronger we could be if ordinary people were united then a lot of people are going to think you're avoiding the question because you are hiding away some sinister statistics that show that in fact migrants are mostly criminals.
Then there is the "overcrowding" or "not enough housing" thing. They don't even attempt to address that directly. Actually I am never sure exactly how to address this myself. There are lots of comments in this thread that do address it: you can point out that there are loads of brownfield sites that aren't used. You can point out that there are parts of the UK that don't have a housing shortage as such, and we could reorient the economy such that there is more employment in those areas. You can point out that governments continually fail to provide sufficient social housing and this is not the fault of migrants. But none of this is really any good to someone with an immediate problem of trying to find affordable housing or housing at all. They don't have the ability to change government policy; even if they did, things wouldn't change on a timescale that would help them with their immediate problem. Therefore, from their perspective, especially in some parts of the UK, it might well be true that their access to housing, in the here and now, is affected by immigration levels. I think that should be acknowledged and not waved away - unless you are able to very directly explain how it is not true. Note that the answer to the overcrowding question in that table literally engages in whataboutery.