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Single market is freedom of movement the EU has said that over and over again.
It would be a new deal as Norway / ukraine have FOM I don't see the UK getting it as Cameron got told to shove it and he had fewer demands... So while not 100% impossible I really doubt it :)
Now of course FOM under EU law can be limited but that won't solve the demand side of immigration. With under 5% unemployment (not all employment great though) I still honestly don't get the hate for FOM.
It's a convenient scapegoat of course...
It reminds me of a similar chart - I'll see if I can find it. That was regarding a proposal for a "two circles" EU. Under that we would sit in a similar position as Turkey.
It shouldn't be impossible for us to have a Turkey + "Access to the EU single market for services". Unfortunately our hapless leaders probably don't have the skill to get that deal.