Ok then, Nigel. Nice clear question. How will exiting the EU give us back our sovereignty or reduce immigration?

Bearing in mind of course that the EU could never pass laws without our approval and the borders have always been under our control. No matter what Farage, Johnson, Murdoch or Rothermere have told you.

No, the EU could pass laws without our approval. With the exception of certain items on which we retained a 'veto', the passing of laws was by a majority vote (or, sometimes a 'qualified majority' vote).
We did not (and, currently, do not) have control of our borders. We are required to allow free passage of EU members across our borders. We can only check that they are actually EU members. We even allowed this immediately for certain 'accession' states (where other states delayed the acceptance of these persons).

Clearly your question is based on a misunderstanding.