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Immigration is not the only issue in the EU referendum – it is not even the top issue for most voters, according to ICM research for British Future’s recent publication How (not) to talk about Europe. But it is still probably fair to say that the main reason we are having a referendum on Britain’s EU membership is, in a word, immigration. The issue remains more salient and more important to the public than the EU itself. Ask most people to describe how the EU affects them and the issues of free movement and immigration are those most likely to come up.

These high levels of public anxiety about immigration may look rather worrying to some. Yet Archbishop of Canterbury Justin Welby was right last week when he said that these concerns are, for the vast majority, not driven by racism. Britain is, thankfully, a much more tolerant society than it was 20 or 30 years ago. While racial prejudice still exists, and needs to be called out whenever it enters immigration debates, those who hold such noxious views are now confined to the extreme margins, with openly racist parties like the BNP effectively dead and buried as a political force.

With net migration at historically high levels people are, however, concerned about the potential impacts of migration on public services, on school places and housing supply, and on their ability to secure a decent job. After years in which migration sceptics claimed that debate was being shut down, that ‘we’re not even allowed to talk about it’, it is now not only debated but effectively on the ballot paper in the referendum.

While Welby’s words on racism made the headlines, his challenge to the two sides in the referendum  – to make this a “visionary” debate – was perhaps overlooked. But his challenge gets to the heart of what would make this referendum a good one for our politics.

Envisioning immigration from the inside...

When Britain votes in the referendum, the public will get to decide whether they want to be part of an EU with free movement. It’s important that this is an informed choice. Both sides need to present voters with a clear and positive vision of what the country would look like if their side won, and that should include their vision of immigration after the referendum. Yet to date neither campaign has done so.

For the Remain camp, when immigration comes up their first instinct may be to try to talk about something else. Yet ducking the issue is unlikely to get them far. Instead they may need to concede that there is no way to guarantee a significant reduction in EU migration while we stay in a European Union with free movement – but argue that this is a price worth paying for being part of the club.

Remain voices could also offer a more practical response, with a plan to manage better the immigration that we have. This could include steps to alleviate some of the pressures on towns and cities where the pace of change brought by immigration has been fastest. We know that the overwhelming majority of EU migrants come to the UK to work, bringing money into the exchequer through the taxes they pay. Yet those economic benefits are seldom seen by those living in the areas of fastest change.

Greater emphasis could also be placed on promoting better integration, with the government setting a civic norm that everyone in Britain for a year or more should speak English or be learning it. It’s well-evidenced that contact between migrants and the settled communities they live amongst is the greatest driver of integration – that attitudes soften once we get to know each other. Yet that is more difficult without a common language. Being unable to speak English also disadvantages migrants themselves, confining them to jobs that are less well paid and with worse conditions.

These arguments will not be enough for some voters, of course. Those members of the electorate whose number one goal is the reduction of immigration are unlikely to be persuaded by any argument from Remain that does not include an impossible promise to end free movement. But such voters make up only a minority of the electorate and do not even represent the majority of those who express some level of concern about immigration. A more nuanced appeal to those undecided voters who are anxious about immigration but who are not entirely hostile could help Remain get past the winning post on 23 June.

...and from the outside

Such difficulties in talking to voters about immigration are not confined to the Remain campaign, however. If Leave is claiming it can offer lower immigration, it will need to show the public a real-world plan to deliver it. That would have to include answers to some key questions. Foremost among them is whether Britain could negotiate a free trade deal that does not include free movement. This is hard to answer definitively before the referendum, because the answer will depend on the negotiations that take place afterwards. But what voters can reasonably ask is what the most important priority for a post-Brexit Britain would be.

At present, it is sensible to assume that a guarantee of free trade access would probably mean a willingness to accept the continuation of free movement, at least for a significant period; while a commitment to end free movement would mean a willingness to accept limitations on trade access. To change that, Leave campaigners would need to produce a clear and workable plan for post-EU immigration policy, and convince referendum voters that it would be an achievable deal that other EU members would see as being in their interests.

Secondly, what would happen to EU citizens already in the UK? Most of the British public will recognise that it won’t be possible to retain the rights of Britons to work in the EU while removing the rights of Europeans to work in Britain. Setting out a clear position on this would not only reassure worried EU migrants living in the UK and worrying about their future; it may also reassure those businesses who are trying to anticipate the impact that Brexit might have on their workforce.

Lastly, what would leaving the EU mean for non-EU immigration? Some voices for Leave have suggested that moving away from free movement may allow a more generous approach to non-EU migrants, particularly those with the skills needed by British businesses. By speaking positively about Commonwealth migrants, Leave voices hope to address the reputational problems for their side from UKIP’s negative reputation among younger and more liberal voters. They also hope to shift what is currently a toxic reputation with a majority of Asian and black voters, who could find some appeal in an argument to rebalance European and Commonwealth migration.

While this may be a politically attractive option for Leave, there is a clear policy consequence of making it. The idea that Brexit makes a more welcoming approach to non-EU migrants possible is a coherent position only if those making it acknowledge that leaving the EU would not, therefore, make it possible to reduce net migration levels to anything like the government’s “tens of thousands” target. After all, non-EU net migration is 191,000 annually – so it would not be possible for this number to increase while also achieving a reduction to the ‘tens of thousands’. Those Leave campaigners offering an immigration policy that would significantly reduce overall net migration numbers, to the kind of level aspired to by Theresa May, the home secretary, would have to argue for more restrictive non-EU migration.

While some Leave advocates may see immigration as their trump card – with Nigel Farage going so far as to say that “the key issues will be open borders, immigration and control” – others have been more circumspect. Key Leave strategist Dominic Cummings, for example, has written that “the official OUT campaign does not need to focus on immigration” on the grounds that the anti-immigration vote is already shored up for their side, while an excessive focus on the issue “would alienate other crucial parts of the electorate”.

To persuade undecided voters to put their cross in the Leave box on polling day, the campaign will also need to show that it can talk about more than immigration alone.

Perhaps the greatest challenge of all on immigration and the referendum, however, is for Prime Minister David Cameron and Theresa May. They find themselves committed to achieving a net migration target of “tens of thousands” while also championing membership of a European Union with free movement that makes this impossible to achieve.

The PM’s attempt to renegotiate his way out of this problem, with restrictions on new EU migrants’ access to benefits, have been dismissed by many as ineffectual. It is true that these measures are highly unlikely to have any significant impact on immigration numbers, as most migrants are attracted to the UK because of its thriving economy and flexible labour market. Yet it would be wrong to discount their value entirely: welfare restrictions would still prove popular with the public, as they offer reassurance that migrants are here for the right reasons. The problem is that they have been mis-sold as a measure that will curb immigration and solve Cameron’s net migration headache – something they will not do.

Beyond the referendum, it may be time to ask whether the net migration target should be revised or replaced with something more realistic that the public can believe in. Whatever the referendum result, there will be a case for a comprehensive immigration review, as British Future has advocated with the Institute of Directors.

That proposal includes a call for greater public engagement in the immigration debate, something that might start to address the collapse of public trust in successive governments’ ability to manage immigration competently. This process of engagement should, however, start with this referendum. The vote on 23 June is a chance to decide a question about Britain’s relationship with Europe that has hung over our politics for 40 years. It is also a chance to have a more open debate on immigration from the EU, a matter of significant public concern. Yet for that debate to happen, both sides will need to set out a much clearer vision of what immigration will look like after the referendum. At present that vision, from both sides of the debate, remains unclear.