Migrants coming to the UK - however they may arrive - is ultimately nothing to do with being in the EU, or not.
The reason we have high inward migration is because the UK has not has a sustainable birth rate for decades now. No other reason.
If people have children at all, it tends to be only 1 or 2, which is not sufficient to replace the population.
(The UN identifies that the replacement rate for a developed nation is 2.1 children per couple - which means couples having 3 in practice, give you cant have 0.1 of a child).
For as long as we have an inadequate birth rate, we will continue to accept high inward migration - its a necessity, not a choice.
But, of course, its better to have a well managed system of accepting desirable migrants (in terms of their language skills, education, values etc) rather than a chaotic unmanaged system.
Being out of the EU means there is more chance of this happening, if the UK - not the EU - has the final say over its own borders.