In Old English, the word "drīfan" has the meaning "drive" in the sense of "pursue, chase, drive out", as in "drive cattle" (run behind them beating their backsides (or just shouting a lot), not sit atop them steering). If I were to say, "Ic drīfe ƿæȝn," it would be taken to mean that I was chasing after the car, or perhaps that I was pushing it. (I suspect that we have that modern sense of "driving a vehicle" through people "driving their animals" while sitting in such a vehicle as a wagon, cart, etc.). In German, they use the word "fahren" (perhaps the transitive "ȝefēran" - "to cause to move", could be appropriate), in Dutch the word "rijeden" or a word related to "steer" ("besturen"). In Swedish and Danish, they have a word for which I cannot find any cognate ("köre" and "køre"). In many of the Romance languages, they have the word for "drive" the same as the word for "steer". "Stēoran" already has a very appropriate meaning, though ("control, steer, direct"), and was already in use in the context of vehicles (boats, specifically). Ƿes hāl! 20:17, 10 Hrēþmōnaþ 2011 (UTC)
Not quite right: drifan is primarily to drive cattle (or fliemendas) forward, which can be a description of what one does to a car, but it used more widely, as B&T lists:
"Sum mæg ofer sealtne sæ sundwudu drifan"
"Hi drifon scipu into Medwæge"
"Ic com mid ðý heáfde and mid handa on ðone stán drífan" (which sounds like a Clarkson headlong rush)
One who sits on a wain is certainly a driver, whether he drives the wain or drives the beast which draws it. I don't know for sure whether it is drifere or drifend or drifa, or whether all are acceptable.
Having said all that, there is the word wægnere if one is careful with the context given its alternative meaning. I would be content with drifere (and Clarkson certainly drifeð those cars to ttheir limits).