It is generally accepted that the battle occurred around AD500 and it was a fight between the Britons and those 'terrifying Saxons.'
Gildas mentions the battle, he describes it as the "....last great victory of the fatherland..." and it did halt the Saxon invasion for another forty years or so. It must have been quite some battle to scare the Saxons away for that long.
Archeologist back up Gildas claim.
"...There is a lack of sixth-century Anglo-Saxon pottery in areas such as Sussex, Essex and Hertfordshire which have all yielded fifth-century material...the Anglo-Saxon expansion in the Upper Thames ceased for fifty years after Badon..." Michael Wood. In Search of the Dark Ages.
Gildas, unfortunately, is his usual vague self when it comes to the finer details. He does not mention Arthur, or where the battle actually took place. What Gildas does tell is is :