The honest answer is that no-one knows for sure. The only surviving pre-Roman instances of Brythonic as a written language comes from coinage minted by certain tribes in the first centuries BC and AD, where the names of local kings are printed in Latin and, occasionally, Greek script. If Brythonic was ever a true literary language prior to the Roman conquest, no surviving texts have been found as of yet.

It is notable, however, that the use of the Greek alphabet seems to have been widespread in Brythonic's sister language, Gaulish, prior to the Roman conquest. Tablets etched in Gallo-Greek writing have been discovered in south-western France, Gaulish coinage often utilised the Greek alphabet (and frequently Greek designs too), and Caesar even writes in his Commentarii de Bello Gallico that the Helvetii kept a census written in the Greek alphabet.

Given the amount of contact between the ancient British and their Gallic and Belgic cousins, I wouldn't be surprised if the Greek alphabet was in fairly widespread use in Britain, too. But that's just my $0.02.

Ogham was a thing, but for the odd inscription, not literature. Celtic languages were very well known for their oral literature, storytellers, and memorizing massive epics and songs. This is a tradition that survives to this day in Ireland, as well as in many other cultures. In other words, like most cultures, literature was a performance art rather than a collection of documents.

Does anyone know when ogham was used?

Robert Graves, in "The White Goddess," speculates about the this conflict that took place between Roman letters and pre-Roman letters. While it seems like some pretty wild speculation at times, his argument is that a Welsh bardic poem details this clash between Roman language and pre-Roman language in the "battle of the trees." He posits that pre-Roman writing corresponded with symbols that represented trees, etc. Read more here: http://en.wikipedia.org/wiki/Cad_Goddeu