SA allows you dual nationality as they have informed you, as long as you apply for that before applying for the second passport (dual citizenship). Have you not already done this if you already hold a Portuguese passport?
As far you already having a Portuguese passport, that might mean having to give that up if you want a British one. For as far as I know and stand to correction, EU citizens are only allowed one EU passport.
If this is the case why and what are your reasons for wanting a second or different EU passport?
As I thought about the same having a SA and Irish passport, now living in Germany. Thought about relinquishing my Irish for a German one, but as an EU citizen already, the ONLY advantage it would give me having a German one. Is being allowed to vote for the national government. As I/we already have a vote in our local authority and the European Parliament.
With your EU citizenship (Portuguese passport) what are the reasons or advantages for applying for a British one? Think you should first consider this question before going through the expense and mountains of admin.