Originally Posted by
AlbaGuBrath
At LHR I’ve found that its quicker to try to use the eGate, then when it fails you’ll be directly taken to a border force person.
The issue that OP has is whether BA will let him board (or not) his flight to AMS with a possible damaged passport and whether the airline he is flying to JNB with (It's not clear if he's returning to LHR for the onward on BA or if he is flying direct from AMS on say KL) will let them board with it as they won't want to be fined by the SA authorities if the OP can't enter SA.
Entering the UK with a damaged passport will likely cause no problems but the Border Force agent will likely advise him to get a new passport ASAP (and in some cases with severely damaged ones they can retain them at the border)