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Related to this, the free movement of labour can hurt the countries which people are leaving as those with skills and knowledge are the ones to go.
This isn't strictly an international issue though. I think there is a good chance that the migration of those who have the skills or knowledge to do well ultimately negatively impacts the culture and politics of the places they leave. Perhaps the rise of the far right in Poland, Northern England, and East Germany can all be tied to this to an extent.
I mean "everyone" who is in the UK/EU.
People need jobs / money/ houses etc
I mean, if people are moving to the UK EU, where are all the jobs for those already and those who are moving here? What investment is necessary to provide decent opportunities for everyone?