There aren't any direct flights that link Glasgow and South Africa, but there are numerous one and two-stop services that you could opt for. The swiftest route between Glasgow and Johannesburg is the British Airways service that routes via London Heathrow and should take about 13 and a half hours.
If, however, Cape Town is your final stop, there is a KLM service via Amsterdam that will have you stepping off the plane in just 14 and a half hours, and a British Airways flight that only takes slightly longer. You can also fly with Emirates to Durban in about 18 hours, so there is plenty of choice on offer. To find the route that fits your trip, consult our flight search tool.
If you'd rather not change planes, you should consider flying direct to South Africa from Heathrow. Virgin Atlantic, British Airways and South African Airways all run 11-hour non-stop flights to Johannesburg, while BA also fly to Cape Town in about 11 and a half, which may suit your trip better.
The cheapest times to visit South Africa are the shoulder seasons between the hottest summer period (November-February) and the July-August tourist rush. The ideal time to take your holiday in South Africa is probably late-March or early-April, as this will give you generally warm temperatures, while still avoiding the worst of the rainy season and keeping your airfares down. Just make sure you book early to avoid being stung by last-minute price rises.