Tom Kibasi writes
“Immigration is such an important issue precisely because free movement of labour is the crucial enabler of the low skill, low productivity, low wage economic model that has been imposed on much of the country.”
This line may be very attractive to the liberal left: it gets to love immigration controls and can begin again to represent the part of working class that dislikes immigration.
The reasoning is attractive. Starve firms of cheap labour, and they are forced to innovate and invest in labour saving machinery and/or in training their workers, which drives up productivity and real wages. In a world where capital is not mobile, that mechanism could work over a very long time period. But when capital is mobile, the firm has an obvious alternative: produce somewhere else where labour is cheaper. Keynes taught us not to make the mistake of assuming output was fixed, and the same is true here. Labour shortages could equally lead to less production, more imports, and a depreciation that makes everyone poorer.
Chris Dillow talked about these issues some time ago. He wrote
“The answer to this set of problems is to increase workers’ bargaining power – which requires, among other things, policies such as stronger aggregate demand and greater redistribution.”
Chris is right. If wages are low because of immigration, that will also mean that wages are unlikely to rise if demand expands. That in turn reduces the level of unemployment at which inflation is stable, allowing stronger aggregate demand and higher output. It is this additional demand that will allow firms to invest in more productive techniques, driving up productivity and real wages.
The endogeneity of aggregate demand and therefore output is key here. We could argue about whether labour shortages would be more likely to encourage firms to invest in labour saving machinery or move production abroad. But there is a third option which can achieve higher investment without running the risk of firms going overseas, and that is to expand demand. At the end of the day the only constraint on demand expansion is inflation, and if immigration is holding back wages it will also hold back inflation. We should not base policy on the assumption that governments undertake unnecessary austerity or central banks make deflationary mistakes. 
The link with austerity is even clearer when Kibasi writes
“What’s more, there is nothing progressive about declining to invest in skills in this country, while plundering poor countries of nurses or doctors or carers and then approaching immigration as if people were commodities to be bought up on the open market.”
This makes exactly the mistake that right wing newspapers have encouraged voters to make, which is to confuse the symptom for the cause. It is not private sector firms that have failed to invest in training nurses or doctors, but the public sector, most recently because of continuing austerity. Once again, what would be the consequence of cutting the immigration option? More money spent on the NHS, or a smaller NHS? It seems bizarre to argue that immigration enabled austerity, and that therefore EU immigration should be controlled. 
There is no evidence that immigration has in practice had any significant (in term of magnitude) impact on real wages. The trend in UK GDP per head had remained remarkably constant until the global financial crisis, despite periods of low or high immigration. The initial years of A8 EU immigration showed no fall in average earnings growth, with real wages continuing to rise. What we do know is that immigration helps the public finances, which means reducing it will mean either lower spending per head on public services like the NHS or require higher taxes.
This point about public services illustrates the real problem with how the government dealt with A8 immigrants. As Nicholas Watt and Patrick Wintour relate, it was not a problem of poor forecasts: the forecasts were not bad once you factored in that Germany would impose transitional controls. It was a problem that the migration was concentrated in particular areas or towns, and nothing was done by government in response. So these towns saw greater pressure on public services, while the taxes immigrants paid went to the Treasury in London.
The data suggests that people in the UK have always favoured lower immigration. I suspect this is similar to questions like ‘do you favour lower taxes’: faced with something that naturally raises questions and concerns, it appears most people would rather have less of it. What began to happen at the beginning of the century is voters started saying that immigration was a key issue, alongside the economy or the NHS. This rise predates A8 immigration, and is strongly correlated with concern over defence/terrorism until 2008.
In truth, immigration is too tempting for some politicians and the media. As Tim Bale reminds us, the Tory opposition quickly started talking about Britain becoming a ‘foreign land’ after Labour was elected. Stories about benefit tourism play upon existing fears, and when politicians join in they appear to validate the problem. If that happens voters can easily turn their concerns about real wages or public services into concern about immigration, erroneously believing that immigrants are the underlying cause. So when austerity began, the government exploited these associations and the media either led or played along. If spending on the NHS was being ‘protected’, what else could rising waiting times be due to other than immigration? As concern about the NHS rose, so did concern about immigration. The truth was that the NHS was not being protected, but that truth was hard to find.
The coup de grace of this strategy was to then associate immigration with the EU, which until the beginning of 2016 had been way down the list of popular concerns. Leavers managed to convince voters that reducing immigration required leaving the EU, even though non-EU immigration remained as high as EU immigration. The Prime Minister and Chancellor, having both pretended that immigration was a major problem, could not turn around and start singing its virtues. In that sense austerity beget Brexit.
As the referendum shows, no good comes from a strategy of using immigration as a scapegoat. The obvious way of handling such a close referendum vote would have been to leave the EU but stay in the single market. But by electing a Prime Minister who had spent 6 years trying and failing to reduce immigration, that option was ruled out because it would preserve free movement. EU immigration may fall anyway as a result of the Brexit and the depreciation it has caused, but beyond that it will be difficult for the government to reduce it further without hitting businesses at a very difficult time.
You do not kill immigration as an issue by talking about British jobs for British workers, still less by pretending that low wage jobs and a decade where GDP per head has hardly increased is the fault of immigration. As I argued here, to allow policy to be dictated by popular concerns risks making exactly the same mistake of those on the left who wanted to embrace austerity, although as I also noted popular concern is more deep rooted in the case of immigration. For that reason, turning the tide on attitudes to immigration will need much more than just facts and figures.
Although that task may seem daunting now, in five years or so it is likely to seem much easier. The chances are we will have left the EU, and the benefits that so many expect in terms of their access to public services or their real wage will not materialize. Either the government will avoid bringing immigration down, or if immigration does fall no obvious benefits will follow and there will be plenty of stories of firms suffering from labour shortages and leaving to produce elsewhere. Arguing then that lower immigration will usher in a period of high wage jobs will seem even more far fetched than it does now.
 A point that opponents of immigration often make is that immigration puts upward pressure on house prices. If there is no constraint on building houses, that in itself is no problem, just as it is no problem that immigrants will need refrigerators or cars. Those who argue that the country is full up have obviously never been to Scotland. Of course it may be a problem that most immigrants will go to English cities rather than Scotland, but that is again an existing problem of regional or industrial strategy which can and should be solved.
 The language of ‘people as commodities to be bought up on the open market’ is really too much. Are people in Poland forced to go and work in the UK? Of course not. They choose to do so, and most are better off as a result. If you want to be emotive then be accurate, and talk about how immigration controls cut off the chance of potential immigrants making a better life for themselves.