From the article you linked (bold is my emphasis):
So what are her reasons? One is control of immigration – and free movement of persons is a non-negotiable condition of the EU for participation in the single market. Here she fails to consider that the European Economic Area (EEA) treaty includes a safeguard on free movement which could be invoked in order to control it. May’s description of free movement includes overstated claims about its effect on public services, ignoring the impact of limited government funding of health and education in recent years – while she cannot bring herself to mention the overall economic benefit derived from EU migrants.
Another is budget contributions. She rules out any budget contributions except for participation in individual programmes. There is no consideration of whether the EEA option – giving money directly to poorer EU countries, with more control over the spending by the contributor – would be desirable in return for increased market access.
Next, there is the role of the ECJ. May states that single market membership ‘would mean accepting a role for the European Court of Justice that would see it still having direct legal authority in our country.’ Let’s not mince words: this is not true. The EEA states are not subject to the ECJ at all, but to the separate EFTA Court. That court has less jurisdiction than the ECJ, and a large number of its rulings are not binding at all. It is only obliged to follow ECJ rulings delivered before 1991.
More broadly, May states that this ‘would to all intents and purposes mean not leaving the EU at all.’ Again, this is not really true. EEA members are not subject to EU rules on agriculture, foreign policy, fisheries, justice and home affairs (except via separate treaties, in part) or trade with non-EU countries – the very issue which May devotes a large part of her speech to.
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So, is the middle ground that makes everyone (sort of) happy just being in the EEA but not in the EU? I think more detail is needed on the options for immigration control i.e. what exactly those safeguards on free movement are. Because that is the main issue that divides people and if there is a good compromise possible there, maybe there is a deal that keeps everybody but the zealots (on both the leave and remain sides) happy.