Most direct flights from South Africa arrive in London at Heathrow Airport - either Terminal 5 (if flying British Airways) or Terminal 1 or 3 on most other airlines. Although Heathrow Airport is only around 20kms from Central London it can take vastly different amounts of time to get into the centre depending on your chosen mode of transport. Also note that some London Hotels and other accommodation providers operate a shuttle service at certain times. As a guide in order of journey time (fastest to slowest):

Heathrow Express is a direct non-stop train from Heathrow to Paddington Station in West London with trains every 15 minutes. This is a great service but could be a little pricey for South Africans spending Rands - a single journey is approximately £16.50. Paddington is on the Circle, Bakerloo and Metropolitan underground lines so an onward journey from there by tube is simple. There are also always black cabs around. Check out the Heathrow Express website for more information. 

London Underground on the Piccadilly Line (dark blue on the tube map) goes from all the terminals at Heathrow Airport into Central London and beyond. The approximate journey time to Leicester Square in the West End is around an hour. It's a great London experience if it's your first time in London and you don't have much luggage. The cost to Central London (zone 1) is around £4.00 with an Oyster card. The Transport for London website is the definitive source of information for all things related to the tube and London buses.

Mini Cabs are licensed Taxis but must be booked in advance. They offer the benefit of a fixed-price fare which you can confirm at the time of booking and obviously depends on your final destination. Unless arranged otherwise, the driver will normally meet you in the Arrivals lounge holding a card with your name on it. The cost is around £25-30 into Central London. If your first stop is a UK Hotel outside of London then it might be worth contacting the hotel to see if they can recommend a local mini cab firm.  

Black Taxi is another iconic London experience - both from the appearance of the car and the experience of spending time with a talkative driver full of interesting stories. If you're unlucky you will get a cabbie talking about the weather for the entire journey. No need to book as loads of cabs are normally waiting at the ranks outside the terminals.The journey is metered (by time and distance) and getting into Central London should cost around £35 upwards. However, if you get snarled up in the notorious London traffic the journey could cost a lot more! 

If you're arriving or departing really early in the morning then the range of hotels in and around Heathrow offer a convenient base from which to travel. There are also some great sights nearby including Twickenham Stadium, Windsor Castle, Lego Land and Kew Gardens.