Dunno about SA relative to airspace on moving maps.
Most places in southern England you have airspace. Whether you are in it generally depends on how high you are rather than where you are in relation to a line, and the height limits are not readily visible on screen.
If it's a biggish chunk of airspace then one or more of the boundaries are most likely off the screen.
What works is your position transferred on to the map, and you're more likely to be able to do that accurately based on a point feature such as a town or village than you are on a line feature like an airspace boundary. Most of the basic GPS units include a database of towns and villages, even if they don't have any graphical mapping info. There's an unfortunate temptation to shave the corners of airspace with a GPS map whereas a properly selected and entered turning point will keep you clear.
To some extent it's the same as the difference between setting off with a map and eyeballing your way and pre-planning your route and turning points and sticking to it. If you pre-plan your route, program it into the GPS and stick to it, then you're less likely to run into trouble than if you eyeball your way on screen, with the added bonus that your workload is lower and you spend more time looking out instead of studying your position on screen.