If you're a citizen of the UK you have the right to live and work in any of the 25 EU member countries, including Greece. So you don't need a permit to work in Zante.
However, In Spain, you are still required to register for an NIE number (roughly equivalent to our national insurance number) and/or a residencia in order that your employer can register taxes etc.
Not sure on the regulations in Greece, but you need to talk to other ex-pats when you get there.