So the "The unrestricted right to live and work in the UK" means you need to have a UK passport?
No.....see previous posts about the nationalities of those going through or those who have gone through the FPP.
Some basic info here for starters:
http://europa.eu/youreurope/citizens...d/index_en.htm
Do I have the right to work in the UK? - Job Opportunities - University of Cambridge
and the BA's own FPP FAQs website will direct you here:
https://www.gov.uk/browse/visas-immigration
In very simplistic terms if you're a national of an established EU member state you almost certainly have the unrestricted right to live and work in the UK. There may also other ways of doing so e.g. family ties to the UK.