Our literary evidence for British, and Celtic generally, chariots is hardly limited to Caesar. If Caesar invented British chariotry than so did all the other authors who mentioned it, including the Greeks--Polybius mentions Gallic chariots a hundred years before Caesar set foot in Britain or Gaul. In fact, our literary evidence is quite enormous, so much so that Latin words for vehicles are often Gallic loanwords, because they had so many different kinds of wheeled vehicles. La Tène burials frequently have chariots in them, sometimes with the charioteers buried as well, and the British Arras culture features warrior burials with cart-like war chariots. For comparison, Germanic warrior burials of the early period feature chariots, but they're replaced by horses and harnesses by the time of major Roman contact. There are images of chariots in Celtic art, including a rather nice situla depicting a chariot race. Between this and the really rather enormous quantity of literary references to British chariotry there doesn't seem to be much reason to doubt the use of war chariots in the historical period among the Britons. And it's not as though the literature is entirely Roman. Greek texts talk of Galatians still using battle-carts and war chariots in the historical period, and the Irish poem the Tain Bo Cuailnge (I hope this bit's right, it's not like I know a lot about Irish poetry >.<) apparently refers to chariots, although it's probably influenced by late antique descriptions of a form of warfare that had long since disappeared from the islands, since it talks about spikes and other imagery that only gets applied to British chariots by late antique authors