Also a welcome from me 6000miles.
I would double check if the UK has no special arrangement for EU citizens with Eastern
European passports. Some western European countries had temporary restrictions because they were afraid of an "invasion" by cheap Eastern European workers.
If there is no restriction your fiance can live and work with no restrictions in the UK. She might need to register with the auhtorities for tax purpose, health insurance but I really don't know how it exactly works in the UK.