Obviously, I know that none of these nationalities existed during this time period, but I was wondering how culturally uniform or diverse the British Isles were before conquest. I know the people were Celtic but I know there was also a lot of variation in mythology and language, as far as I can see from Wikipedia.
There is very little hard evidence about the spread of nationalities that existed in this period. What we can infer comes mostly from language evidence, and whatever the Romans wrote about them.
Language in pre-Roman Britain and Ireland is usually separated into two distinct Celtic groups - Britonnic (British) and Goidelic (Irish). Britonnic is the linguistic ancestor of modern Welsh, Cornish and Breton, and was spoken all over Britain. Goidelic is the ancestor to Irish, Manx and Scots Gaelic, but at this time was limited mostly to Ireland proper.
The best contender to a third "nationality" would be the Pritanic (Pictish) people of northern Scotland. However, they spoke a dialect of Britonnic (or at least a very close relation).
Both the Romans and the Irish referred to the Picts under the blanket term "Britons", and the idea of them being a distinct culture doesn't seem to emerge until 200 years after the Roman invasion. Indeed they had differences from tribes in southern England, but they in turn were different from the tribes in, say, north Wales.
It seems a schism happened during the Roman occupation of Britannia; the Britons within Roman borders became increasingly Romanised whereas the Picts retained their old ways.
Neil Oliver's "A History of Ancient Britain" is a really great read if you want to learn some "entry level" in-depth info about the fascinating and under-studied people of the pre-Roman era.
Genetically speaking you may want to look at this genetic map of Britain prior to the 20th century.