They had no control at all over EU migration, basically. They are not part of the Schengen Area, which means that they have their own visa regime (with respect to non-EU nationals), and they have systematic border controls (passport checks) at their borders (air, train and ferry terminals, since they don't have a Schengen-Area land border). The main content of the Schengen Agreement is the removal of systematic border controls.

The free movement of EU persons (and their families) holds in the whole EEA, independent of the Schengen Agreement. There are also EU rules about where refugees are settled, but the UK already had an opt-out from those.