If you are a full UK citizen (not an 'overseas citizen' or any of the other half-baked categories), you can indeed choose to work and reside in any of the EU countries (there are exemptions for the new accession countries in the east, their citizens are slightly more limited in this regard).
Depending on the country you are planning to move to, you might still have to register as a resident and obtain a work permit. But as a EU citizen you have a right to obtain such a residence and work permit and it is typically a formality.
