Poland is largely Catholic, remember the unexpected election of a Polish Pope around the time of Lech Walensa. This was building momentum for Poland to exit the Soviet Union and less than thirty years later they are being told to accept 'third' world immigrants with a different religious culture possibly violent to other religions ( the jury is out on this one it is not black and white IMO).
I do accept the Polish immigrants would need some thought though surely Germany, France and others would soak up some of that excess labour especially if they take business from the City of London.
I agree the richer countries do pose the bigger risk unless Britain reaches out to the likes of Poland behind back doors to force their hand for what
@PedroMendez eloquently poses above as the possible move towards a second tier 'flexible union'.
Re Italy I don't think they have been facing the immigrant crisis for years and years, I think that has been Greece yet I do agree they have that problem in the last couple of years and that larger nations should have been lending a hand. I think the problem was there was a political mindset to allow this immigration into the EU. Cheap labour or other less obvious and possibly sinister motives, I'm not sure. On the surface what seemed strange was that a lot of the asylum seekers all had modern phones showing them the route to take. For me it suggested certain NGO's were encouraging this and dishing out phones with instructions. Italy is primarily a target because the West decided to take out Gadhafi and Libya is close to Italy.
The West has never wanted Africa to be successful and EU loans to Africa had strict conditions and coincidentally Gadhafi was hoarding gold with the intention of setting up a Pan-National African Bank.
I don't think the Brexit immigration factor was just about Eastern European immigration I think it was just against large scale immigration from everywhere yet any debates about this turned towards the ECHR as telling us we could not stop it, so in people's minds the EU was seen as the barrier to preventing all types of immigration and not just from the EU. I don't think most people are against foreigners it just seems too much has happened too quickly.