What is this cheap labour that you speak of? The stats show that EU migrants are, on average, significantly more qualified than the native population. That's the reality. You have seasonal labour in agriculture, and I strongly suspect that concessions will be made on that front, whether it's from European or non-European sources, but the bulk of EU migrants are highly skilled, and highly sought after.
To coin a phrase at the moment, the reality is that no immigration policy (ie free movement via the EU) is better than a bad immigration policy (ie what we have with the rest of the world). Those migrants we have no control over are, on average:
- Younger (and thus having fewer calls on the NHS)
- Fewer dependents
- Better qualified
- More likely to have a job
- Paid more
- Less likely to claim on welfare
It's something that frequently baffles me, as we have control over migrants from outside the EU already, and the ones the government let in tend to be worse than those we have no control over.