Free movement of workers has become one of the major stumbling blocks in Brexit negotiations. While most economists see continued access to the single market as crucial for the UK’s economic prosperity, the EU has consistently stated such access is not possible unless the UK accepts EU rules on free movement of workers. In other words, if you want to be in the club, you have to accept all of the rules, including admitting EU immigrants. This places UK negotiators in a difficult bind. The EU referendum result is widely seen as a clear message the British public wants to "regain control" of immigration policy. So how – if at all – can the UK stay in the single market while addressing public concerns about EU immigration?

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One possibility that has been mooted is introducing some sort of "emergency stop" to EU immigration. The idea is the UK might stay in the single market – either as a full EU member, or as a member of the European Economic Area EEA (the "Norwegian model") – but be allowed to impose a temporary cap or stop on EU immigration. So far, the noises from Brussels and other EU capitals have not been encouraging. EU governments and the European Commission have suggested free movement of workers is not negotiable – it is a core condition of participation in the single market. But there are a number of precedents that suggest such an approach is not unthinkable.

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First, the EEA agreement already includes "safeguard measures", permitting its members to limit EU immigration if serious economic, societal or environmental difficulties of a sectoral or regional nature arise and are liable to persist. This has been invoked by Liechtenstein, which currently has separate arrangements enabling a cap on levels of EU immigration. Of course, Liechtenstein has a population of just 370,000, so faces a much greater risk of influx. But it suggests there is a precedent to build on. Free movement is indeed negotiable.

Second, EU states are already entitled to introduce transitional limits on free movement of workers, in cases where a new country joins the EU. These provisions allow states to limit free movement of the nationals of the newly acceding state for up to seven years. Interestingly, after the first five years transitional provisions for a further two years must be justified based on "serious disturbances on the labour market, or the threat thereof". So again, we find an example of labour market concerns justifying an exemption to the free movement of workers.

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The third precedent is the emergency stop on welfare access, negotiated by David Cameron in February this year. The "alert and safeguard mechanism" foresaw limiting access of EU nationals to in-work tax credits. This was to be justified in cases where immigration "leads to difficulties which are serious and liable to persist in its employment market or are putting an excessive pressure on the proper functioning of its public services". It was assumed the UK would be deemed to meet these criteria – suggesting there would be a way of formulating criteria justifying an emergency stop in a way that the UK would qualify.

The main problem with this approach is its necessarily limited duration. Seven years seems to be the magic number for restricting EU immigration – and it is very likely a similar period would be tabled for an emergency stop. Yet seven years may not be enough to assuage Leave supporters’ concerns about immigration control.

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The dynamics of EU immigration suggest such a stop might have a longer-term impact on mobility. Immigration flows – especially of low-skilled migrants – tend to be heavily influenced by "migrant networks". Communication and support between people in sending and destination regions make migration less risky, and can encourage an increase in flows: once migration has started, it often becomes self-perpetuating. Curtailing such movement over a period of several years may suppress these effects. In addition, immigration flows from Central and East European countries appear already to be declining, while inflows from Mediterranean countries affected by the economic crisis may have improved within the lifetime of the programme – assuming, say, five years for its negotiation and a further seven for its duration.

But would such a compromise be politically acceptable? From the EU perspective, given the precedents in EU and EEA law, it doesn’t seem to represent a radical departure from current provisions. It may be more politically palatable if it is part of a deal for EEA countries rather than full EU members. The EU is concerned to make sure its members are not allowed to "cherry-pick" the provisions they like.

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The sticking point might be selling it to the UK public. The government would need to make a strong case for why staying in the single market is so important. And they would need to convince many voters that such a measure would, indeed, imply regaining "control" over immigration.

Christina Boswell is Professor of Politics at the University of Edinburgh.