Google Books turns up dozens of relevant examples: “I never drove. Never." "I never drove a Cadillac; I drove a Pontiac." "I never drove to Florida,” he said. "I never drove any eighteen wheelers, but I drove a sixteen wheeler.” "I never drove after I started drinking; though I drove hungover plenty of times." "I didn't know my way around the city—because I never drove, I never learned the route to the George Washington Bridge or Midtown Tunnel." " I never drove a horse nor held reins in my life." (an 1868 example, others are modern)

I'm a US native speaker. Personally, I would be much more likely to say "I've never driven," but I think "I never drove" is correct, and common enough that I honestly don't even notice it and can't say exactly how common it is. I think it's correct and quite frequently used. It is very natural if it is said at the exact moment that someone is driving for the first time. Someone steps into a car and sits down at the wheel and says "Wish me luck! I'm excited! I never drove a car before." It is also very natural if it is followed by words that explain "before what?" For example, "I never drove a car before automatic transmissions became common, so I never learned to drive a stick-shift." Admittedly this is over a century ago, but Emily Dickinson wrote: I never saw a moor, I never saw the sea; Yet know I how the heather looks, And what a wave must be.

That's interesting. Before I came to the US I used to hear that construct (and ones like it) in US entertainment all the time. It sounded novel and unusual (and therefore cool and memorable) to me, because I wouldn't hear British people using it. Similarly: "No, I didn't see it" (US) and "No, I haven't seen it" (UK) mean the same thing about whether or not you've seen a movie. I've been in the US for 11 years now and my answer would be, yes, it's correct in AmE, and probably also now in BrE given the influence.

I HAD never driven a car or I never DRIVE a car

American English, needs capitals.