How will that control work however if we are to trade with the world? As an example, the current deal being done between Canada and the EU involves far more 'non-tariff' aspects to it than tariff reductions/removal. That basically means things like greater unification of regulations and standards, or as you put it, Canada exerting control over Europe, and vice versa.
This is largely the tip of the iceberg as well. Consider that services make up something like 70% of the UK economy, yet services are largely excluded from not only the EU trade area but also most multi-lateral trade deals around the world. Given the prominent role services play in the modern economy it seems inevitable that these will be slowly included in trade agreements, and indeed the EU are trying to do just that, but it is slow progress because folks (and lobbyists) grumble about sovereignty being taken away by centralised bureaucracies.
Which do you want? Free trade or local control? I'm not sure you can have both.
Who is to say people coming here are slaves though? Even if they are relatively low paid, I suspect the vast majority come here willingly. I personally know quite a few people, for instance, that took low paid work initially whilst they learned the language. All are in decent jobs now, with a good number having taken degrees here to help them do so.
Even a (Czech) builder mate of mine was grumbling the other day that work in the Lake District was only giving him £150 a day, which is a decent whack higher than the average wage, especially outside of London.