Depends on the person asking, if you want to continue speaking to them for the rest of the evening (or whatever situation you're in), or you just want them to go away.
If the latter, then saying you're a minicab driver works best. Most people will ask you the usual "are you busy?", "is it good money?" etc. Just say, "I get by nicely, thanks, and it pays the bills".
Saying you're a chauffeur, (whether you are or not, if you're working for a chauffeur firm, or just drive for one client), isn't recommended, as you'll get the usual "do you/have you ever driven anyone famous?" which I find annoying (obviously, a professional wouldn't say who their client/s are to strangers), other than that, you'll get people asking what car/s you drive, where you go, and other questions which may seem impersonal and feel uncomfortable answering.