Earlier quoted context omitted.
Once you have a Visa/Residence permit (work) in one country you can freely move between all the EU countries. (I live in Italy with residence permit, so I know)
Usually you need a permanent residence permit (Greencard equivalent), and then it has to be a fairly recent one as the laws were only harmonized in the last 5 years. And even then, the permit for most of the EU isn't valid for the UK or Ireland. In Germany the first permit that you get (an H1B equivalent) is tied to one job, and hence, tied to the place where you have that job. After 5 years of working full-time (and…
However you can still (with the permit to stay) move between UE countries, just get back to Italy and declare revenue (as entrepreneur).