>It's free movement of labour between EU member states.
That distinction is kind of meaningless when thousands of people can enter several EU member states pretty much unregulated, then disappear under the radar and go anywhere within the EU.
UK is NOT a Schengen country. There's a border under British control.
That may be possible in, let's say, Belgium. Someone enters through the Italian border, somehow tricks the border patrol, and then can go with no problem from Italy to Belgium.
That's not the case for UK. On enter, you need to cross a border with officers, customs, etc. You can't even cross the border unnoticed through Ireland, as Ireland is also not a Schengen country (there's no border between Ireland and Northern Ireland, though there are sometimes checks from Police in buses and so on). There's a border also in Gibraltar...
The Brexit campaign was mainly complaining about workers from Eastern Countries like Poland or Romania, where they have the legal right to move and work in the UK, due EU accords. Plus fear that Turkey may enter in the future.
That distinction is kind of meaningless when thousands of people can enter several EU member states pretty much unregulated, then disappear under the radar and go anywhere within the EU.