Can you keep both " British Passport and Portugal Passport " ?

Needless to say, you cannot get a British passport unless you're a British citizen. Nothing in what you say suggests that you are. So first things first, find out if you can become a British citizen. If you're successful in that, you can then apply for your first British passport.

And yes, both the UK and Portugal allow dual/multiple nationalities, so you won't have to give up your Portuguese one (nationality or the passport that goes with that) if/when you become a British citizen.

First you would have to apply to become a British citizen, only then can you apply for a British passport and of course you can have dual citizenship with Portugal and the UK

Yes, you can be a dual citizen of both the UK and Portugal.

To get a British Passport, you need to be a fully fledged British Citizen, and the passport will be a European passport which allows you freedom of movement between EU countries, of which Portugal is one. So you really do not need two passports.