But it does. In fact it has to over control non EU immigration to try to make up for the uncontrolled EU immigration. Witness the people in this thread moaning about us not letting enough Aussies in.
No it does not really do it. Otherwise there would not be 290K non EU migrant each year, including non skilled. (heck the net EU flow is only 190K vs 195K the rest ; December 2016 ONS numbers :
net migration = +335,000 (similar to YE June 2015), comprising +189,000 EU citizens, +196,000 non-EU citizens and -49,000 British citizens).
It could reduce it drastically, but does not do it. That is why the pretension that UK needs to reduce EU migration are a fallacy. If it was that much a problem the non EU flow would be the first to take a hit. But while it reduced proportionally to EU, there was not really that much restriction added in the last what , 2 decades ?
Furthermore the UK as you keep pointing out do a lot of exchange with the EU, on trade goods, services, and yes passporting right for financial institutions.
You would
expect that there would be a lot of going around with your major trade partner.
Again, the impact estimated by unskilled folk on the UK economy has been estimated as very low , less than 1 % as cited by study up-thread, that you will undoubtedly reject.
Furthermore it seems the EU migration are rather younger folk, tax paying, and consuming. They are not the one filling your hospitals, or putting the service to test. The one doing that are your own government deciding quite strange things in the last decade (wasn't there a change to have doctor/hospital competing for finance ?), and simple demographic that the UK population is aging.
And.... That is why the things about EU migration is BS.