International and EU passport, which do i use for living rights?

Im asking on behalf of my girlfriend, she holds an Italian passport and a Uruguayan passpor, shes looking to either move to or study in the UK to live with me, in regards to living in the UK or working here, can she use her italian passport and therefore enter as an EU and abide by the EU laws?

She lives in uruguay not sure if that makes a difference, any help would be appreciated