I'm referring to common immigration policy, i.e. from outside the EU into the EU. This is distinct from freedom-of-movement for EU citizens within the EU. Such freedom-of-movement does not apply to non-EU citizens.
The UK manages to both have influence over EU immigration policies AND also have exemption to it for non-EU immigration, AND can apply its own limitations even for when immigrants get citizenship for a limited period. Yet many brexiters spout on about how the EU just dictates everything to us and it's all out of our control. Absolute rubbish.