Is there any real appetite for that in the rest of the EU, though? You need some kind of potential partners to put together significant reform of a 28-member bloc, and restricting the free movement of labour would be a huge change. I could see it happening if there are increasing questions in many EU countries about it, but not if there are only really increasing questions in one.

External immigration is a huge issue in many parts of the EU, and a common rallying point for the anti-immigration right. Especially Muslim immigration has become a major political issue in many EU countries. There is probably a coalition that could be put together with a hard-line view on refugees and external immigration (and one is sort of forming in opposition to the Merkel-led coalition's more accommodating view). But internal EU movement is a much smaller political issue in much of the rest of the EU (though it is a big issue in non-EU, but Schengen member Switzerland). Anti-immigration parties elsewhere in Europe, like Sweden Democrats, are mainly animated by worry about Muslim immigration from outside the EU, and don't really have the beef with e.g. Polish immigrants that some of the UK anti-immigration groups have.