Would leaving the EU reduce migration to the UK?

The UK already has full control over migration from non-EU countries, and this would not be affected by leaving the EU. However, leaving the EU could reduce levels of EU migration to the UK. In practice, it would depend on what arrangements were negotiated between the EU and UK post-Brexit. If the UK joined the EEA, or substantially replicated EEU arrangements (as Switzerland does) then relatively little may change, as free movement would continue to apply. But if no or only limited trade-related agreements were negotiated, the position would be similar to that prevailing now between the EU and other advanced countries like the US. Migration of EU citizens would be reduced, seeing as those who wished to work here would need to qualify for a work visa, most likely via the existing system in place for non-EU nationals. EU citizens already resident in the UK would likely be permitted to stay; no significant  figures on either side of the debate have suggested otherwise. However, considerable ambiguity remains. What would be the cut off date? What would be the position of EU citizens who have resided here in the past? Given that the UK has no population register and does not record movements of EU citizens comprehensively, determining who qualified for permanent residence rights would be hugely complex, both legally and administratively; a considerable period of uncertainty is likely.