The three major centres of South Africa are Johannesburg, Cape Town and Durban (in that order of size). Flights from Birmingham to Johannesburg and Birmingham to Cape Town have at least one stop, whilst flights from Birmingham to Durban have at least 2 stops.
If your plans are to fly to Durban, first fly from Birmingham to Johannesburg (or Birmingham to Cape Town), and then catch a local flight from Johannesburg to Durban (or Cape Town to Durban). The links below contain a full list of airlines operating flights on each route and links to their online flight reservation systems.
There are more airlines operating flights from London to South Africa, than from Birmingham. You may therefore wish to see a list of airlines operating flights from London to South Africa.