An ex of mine gained indefinite leave to remain in the UK based on her grandfather having been born in the UK. Essentially this was a stamp in her kiwi passport and enabled her to come and go as she pleased to the UK and work unrestricted BUT again in the UK only. After 5 years she was entitled to to apply for naturalisation as a British citizen and then in turn send off her certificate to apply for a British passport at the passport office. It was only after gaining this passport that she could freely live and work throughout the EU.
If you fail to have a parent or grandparent (think only a grandad!) who was born here then the only other option is a work permit and to seek sponsorship. Then it is a similar process to the above except after 4 years you can shift off the work permit and apply for leave to remain in your own right which means you would no longer be tied to your sponsored employer. Believe me working 4 years for the same outfit can be a long long time when you want to be somewhere else earning more money but have invested so much and are within a whisker of getting the passport. After 5 years its naturalisation and the passport and then the EU will be open to you.
Much easier to marry an EU citizen if you ask me and avoid the hassle!