Lets take this logically - purely by reading tawdry press at times - he has a new baby presumably with a British citizen? therefore he (if south african) cannot be deports on human rights grounds as he has a child here - however just because he can stay, (if he is south african) then it doesnt automatically follow that the first children can - the depended and earning powers would come into play.
Has that made it clearer or muddied the waters?
I still think he's English though, otherwise, why would you leave south africa and arrive here? Unless - he is south african, because maybe his parents worked out there for a large proportion of their lives and retired back in teh UK? but then, I cant see people doing that unless (a) they ran out of money (b) they need specialist medical care, when you have you children and grand children in south africa.
So on balance, I think he's English, the wife killed herself, he brought the kids back here, dumped them on his parents, set up a new family and forgot to sort out the visa.