There is left-luggage at all terminals in LHR: http://www.excess-baggage.com/airpor...l_services.php

You don't say whether it's JNB or CPT you're heading to; I think they're out of different terminals (T1 & T4 respectively). CAI is served from T4. It's quite feasible for you to leave luggage there on your way to CAI and pick it up on return for check-in to SA. If you're travelling in J or F (or are BA Gold), you'll probably be heading to the arrivals lounge at T4 on the return from CAI - the left luggage is right next to that.

I'd say it's certainly worth doing this compare to the alternative of lugging it to CAI & back for no reason.

Edited to add: Something to try - perhaps stay at the T4 Hilton one night when you're first in London. They may be willing to store the bags for you (you can only but ask!).