If you hold a UK passport, you're entitled to live and/or work in any of the 27 EU member states, including Portugal.
Obviously, wherever you live, you need some sort of income to pay for your accommodation and living expenses. However, there's nothing to stop you moving to Portugal and living on your savings while you try to find a way to make some money. (i.e. you don't need to have a job before you go).
I saw an episode of A Place in the Sun last week and there was a woman who bought a two cottage's for �104,000 in rural Portugal. She can live in one and rent the other one out. It looked very tempting. It was in a rural location though as you can tell with what she paid and I did not know when the episode was made, it could of been last year then again they showed an episode yesterday and it said prices based on 2003/4. I thought I could sell my house, buy a flat here and buy two rural cottages in Portugal and live off the profit. Not bad if you got someone to rent the cottage in a rural area.