Funnily enough, I think the Britons were just and off-shoot of the Gauls and Belgae who migrated over to the Isles not long before Caesar's conquest of the former. It is interesting though, because I understand the Gaels came over from Spain, and Cymric peoples appear to be more closely connected to this group. Chances are Boudicca had more in common with Vercingetorix's Gauls than with the nations she was depicted as ruling over in CIV5, based on city names.
Yes, I'm familiar with the theory that Gaulish and Brythonic represented a dialect continuum. I have no position on that particular theory: I can see the arguments, but I think our material (particularly our Brythonic material) is too scant to make a conclusion. The languages you describe as "Cymric" (by which I presume you mean Brythonic--i.e., Welsh, Cornish, and Breton), however, are direct descendants of the language of the Britons, various also called Brythonic or else Britonic or British. Culturally, though, Boudicca would have been closer to the Gauls--especially at that point, since both Gaul and Britannia had been thoroughly Romanized. As for the Irish coming from Spain, Gaelic is definitely
not related to Celtiberian (well, not any closer than it is to any other Celtic language; it's hard to say how close Goidelic and Brythonic are after centuries of close contact--what appear to be shared innovations may be the result of language contact); most evidence points to Goidelic being autocthonous to Ireland. It's worth recalling that Irish legends also connect them to the Iranian-speaking Scythians...
The cladistics of Celtic linguistics are a nightmare. There's a very strong case that the Celtic languages are related, but exactly how they relate to
each other is problematic. The divisions of "P-Celtic" and "Q-Celtic" are unhelpful: the P-Celtic languages (Gaulish, Brythonic)
might be related; the Q-Celtic languages (Goidelic, Celtiberian) are not. This is complicated by the fact that some Gaulish inscriptions appear to be Q-Celtic. Some features of Celtic (loss of /p/, /gʷ > b/, /ē > ī/) could easily be areal features, which is a theory that I understand to be growing in popularity (i.e., that the Celtic languages are in fact three different unrelated branches: Celtiberian, Gaulish, and Insular Celtic); personally, I think that's premature.