Upvote:5
If South Africa has exit controls, use your South African passport when you leave the country as this will match South Africa's records.
When entering the UK, present your UK passport and take the EU citizen line. You may get questioned as to your situation. If so, just be honest. "I'm a South African citizen who recently discovered I was entitled to a UK passport because of my father, so this is the first time I'm using my new UK passport." There will be absolutely no trouble with this.
My brother-in-law is American and recently got his Canadian citizenship. On his first presentation of his Canadian passport at Canada customs, the immigration officer congratulated him on his citizenship and shook his hand, to welcome him to the family, as it were. So have no trepidation here. If anything, this will be a positive, not a negative.