The EU makes all those countries that are part of the organization to be borderless and allow anyone and everyone they want.
This is both more false and more true, than you'd think - when coupled with the migration scare.
As you just did.
So - the UK done fucked up, during the integration period of Schengen, when open borders (like in the US ('merica fuck yeah), between states) became a thing.
They were the only major country in the union (aside Luxenberg and other 'heavy weights')) that didn't implement an optional, and legally and politically viable transition period, but rather said OPEN BORDERS! from day one.
That backfired, and they got more influx from willing (EU citizen) working migrants, than they expected. A few years down the road, racial tensions spiked because of that. ("Our social system moneys only for UK born citizen!" - meh, isn't allowd under EU regulations for good reasons. (Free market on wares also has to lead to a free market on labor, otherwise, all the moneys ends up in the big countries, even more so than it already does.)
Then came the "migration crisis" of 2015+ (people outside of the EU fleeing into the EU).
No internal borders in that case - first wasnt true. The Visegrád countries at certain points closed their borders for migrants entirely (violating Schengen). Outside borders were strengthened and more tightly controlled (mediterranean sea) also.
Furthermore - when 'simply wave them through' events took place, it was on behest of gouvernments taking the influx, so voluntarily, while there still where 'impromptu' border controls being set up again.
(Countries did 'take the load off of others' because of political considerations, and because of the industry in germany liking the idea of more cheap workers - basically.)
The most important thing to understand though is - that 'getting' into another country as a non EU migrant -- isnt the end of the road. Because based on your cause of entry, you get registered, helped on humanitarian grounds for maybe 1-2 years, and then sent back, based on your cause of entry and nationality. You dont necessarily get a permanent living or work permit. And if you travel between countries, you dont get your social payments from that country either, so you better travel back, without you being allowed to work. So, borders or not... Don't matter that much.
Furthermore, during the migration crisis of 2015+ the UK controlled the channel (border between France (EU mainland) and the UK) tightly - regardless of Schengen. So the UK had not had an influx of migrants during that period.
If you are a dumbfuck, and are reacting based on emotions - and were living in germany at the time, you became more populist/racist, when seeing, that germany was overwhelmed for a time with getting through the administerial stuff of registering new migrants. In certain cities. For about three months. Because of a lack of preparation. And a message that spread on social media ('everyone is welcome') that wasnt intended to produce what it produced at the time. That problem is solved already. Also following that - tighter controls on EU outside borders where implemented, and could curb the migration flow to managable levels, to this day.
So if you ever see a dumbfuck posting RT propaganda of people with darker skincolor jumping off a boat, understand that - NONE (+/- a few) ever ended up in the UK, none of them stayed permanently - if not on grounds of asylum - and sending them back WORKS, unlike in the US (southern border), because crossing the sea border is expensive and more dangerous, than crossing a land border (people from the source countries are selling their homes to get here).
'Working borders' as the UK had in place during the migration crisis (violating Schengen, but no one other than NGOs complained, certainly not the EU) would only serve one purpose, and that is to create a humanitarian crisis (people getting gunned down, starving), in countries that could least cope with that at the point in time. That regime (have the countries on the outside of the EU deal with it) works in 'normal/peace' times, but not - if you've got a migration crisis at hand. Or it gets ugly - quick. (Countries all over the EU told germany - open your border, or we let them through regardless. (Instead of gunning them down.))
Its much more sensible - to let the flow move on, when its there already, try to cut off incentives, causes, and increase difficulty for latecommers, and then deal with the people who came - according to your laws, afterwards. And over time.
People without a residence and without a work permit, without papers, have a MUCH harder time getting by in the EU than in the US basically. In short, its pretty near to impossible to do so an live an even close to normal life. You need papers for everything within the EU. So eventually those people register (looking at the numbers). And if granted long term asylum - thats also non permanent. The first generation most often is fucked. (Second generation less so.)
So if you are here to post effing "people with dark skin jumping from boats" propaganda as the cause for the UK leaving the EU - NONE of that was ever true, and this was the UKIP camp brainwashing idiots with no education. Based on emotional motives. (Fear.)
The truth is - all of our societies have ways to handle extreme events with reducing "humanity" in the process, and ignoring active law (Schengen), when push comes to shove - with no one ever going to court with each other over that (laws are written in a certain way).
Regardless - yes, EU means free inner european migration for EU citizens. You cant complain about that either though - unless you are a nutter - because thats the basis of an economic union that isnt a 'colony' ('lets bleed out the economically less viable countries').
We have gone over that three times in this thread already. Keep your opinion, your feelings, and your russian videos of people with dark skin jumping from boats to yourself. Dont spread propaganda.
If you believed in that being a reason for the UK leaving the EU, you've been had.
(Germany or France structurally have no different position on 'external' migration than the UK. Its just that the UK are an island, and will always behave like one when it best serves them. If you then look at if that resulted in pushback from any of the EU countries - hardly ever. Still people got sold on this being a deviding issue. On the day before they googled "whats the EU". (The day after the referendum.))