If Britain votes to leave the EU it will be because of hostility to immigration: that is the conclusion both of the UK press (from the Sun to the Financial Times) and of the political scientists who spoke at NIESR’s recent conference on the topic.

But it is also increasingly apparent, whichever way the UK votes, the impact on migration flows – and in particular on free movement of workers within the European Union – will be minimal, at least in the short term.

On the “Remain” side, only two years ago, the Prime Minister, in an article entitled “Free movement within Europe needs to be less free”, wrote:

Britain, as part of our plan to reform the EU, will now work with others to return the concept of free movement to a more sensible basis.

Instead, the Prime Minister now claims that he was, all along, a strong supporter of the principle of free movement, writing last week in a German newspaper that:

like Germany, Britain believes in the principle of free movement of workers

After this U-turn, as we all know, the Prime Minister’s renegotiation now focuses on some complicated changes to entitlements to in-work benefits that may or may not simply amount to restrictions we could have imposed ourselves all along; and that will, in any case, have little or no impact on migration flows. So, if the UK votes “Remain”, it is reasonably clear free movement and immigration will continue more or less as now.

What about if we vote “Leave”? Well, as I wrote here, in theory, the UK would have more flexibility outside the EU. But I also pointed out that the two other large European countries that have full access to the European Single Market – Switzerland and Norway – both accept free movement of EU workers; and that indeed, the Swiss, having voted to restrict immigration, are now being forced to think again by the threat of losing Single Market access. So - assuming we do indeed want to stay part of the Single Market – significant changes to free movement are far from a foregone conclusion even if we do in fact vote to leave.

So far the “Leave” camp has mostly tried to dodge this question, arguing either that the referendum is just about “taking back control.” This is the approach of the Vote Leave campaign, whose website barely mentions immigration, and certainly says nothing about what UK policy towards immigration and free movement could or should look like after Brexit.

What about the other main “Leave” campaign, “Leave.EU”? Well, their website states that “Leaving the EU would give us back control over our own borders”. Indeed, the front page offers visitors a chance to vote for “what excites you most” about leaving the EU, and this is the most popular choice by far.

So it would seem that this wing of the “Leave” camp (which is more closely associated with UKIP leader Nigel Farage) does indeed intend to make free movement much more central to its campaign – implying that a vote to Leave is a vote to end free movement.

Except that, just a few days ago, it was announced that Leave.eu would be adopting a version of the so-called “Flexcit” approach to Brexit. There is a lot more detail on “Flexcit” here, but the key idea is that it accepts, as an interim measure, some version of the Norway option in respect of both the Single Market and free movement:

A less ambitious solution, which keeps us in the Single Market and allows freedom of movement (but with improved controls) might deliver a successful referendum outcome.

So any substantive changes to free movement will have to wait, perhaps indefinitely:

Once we are no longer members, it will be possible to work on a longer-term settlement which seeks to modify the freedom of movement provisions.

This U-turn has not surprisingly caused some confusion in the Leave camp: here’s a recent twitter exchange:

Anyone noticed @LeaveEUOfficial has suddenly stopped talking about immigration? It’s because their new Flexcit plan accepts free movement

@LeaveEUOfficial: Vicky, it's still very much on the agenda. Flexcit is the foundation of an exit plan that we are working on. We hope to be able to give you a proper update in the near future but rest assured, we want to leave just as much as you do!

Which effectively concedes the point. So where do we stand? Bizarrely, we are approaching a referendum where most of the main protagonists have, at some point, claimed that the main issue with the current functioning of the European Union was free movement of workers; and yet none has a clear plan on when and how it should be modified, in or out; and, even if we do indeed vote to leave, the prospect of change in the near term seems to be receding steadily. It looks like free movement is here to stay.