One quick note, not sure if you have right to work in EU, if this gives you right to work in the UK.
As I know in the opposite case, living in the UK, and my wife had UK visa, she needed a Schengen visa to travel within the EU, so she would not have right to work in the EU, just UK.
So you might not be eligible to work within the UK, because UK are not within Schengen. If you have EU passport, then this not a problem, but takes 5 years to get a EU passport, only 3 to get UK passport.
You should check a couple of the immigration forums, they will know this better than on these forums.