I believe this is largely about the migrant crisis, citizenship or a passport granted in any EU member state allows unfettered travel among all EU member states. Britian just bowed out of that asinine arrangement.
The problem for Italy is they are the primary entry point to Europe for North African migrants via the island of Lampedusa. Italia can only hope the migrants do continue on to other parts of Europe.
Unfettered immigration was specifically noted last night as I sat up late watching the aftermath on BBC1. One of the BREXIT proponents cited hugely negative sentiment as to what this wide-open influx of humanity has wrought upon working people across the UK. Mostly, they want to be able to speak truthfully about it without being immediately dismissed as a racist nutter, which sounds all too much like someplace else in the world I know.