I prefer to think Brythonic, just from the appearance and the romance of it, but that's a bad reason scientifically, so I'll stick with the more generally-accepted form Brittonic. The Brittonic languages are a substrate of the English language which were largely overrun by Anglo-Saxon elements from the 6th C on. They are Celtic, and related to but not the same as the Goidelic languages that became what we currently call Celtic. Their relation is farther back.
All this comes up because of Grim's interesting post about Anglish, a fun exercise in imagining an English more fully Germanic, uninfluenced by Norman French. I have written about this substrate before. In fact, the discussion of hydromyms, especially rivers, is one of my oldest posts. It belonged originally to a now-defunct blog I had before this one. If you like this sort of thing at all, check that link, which includes a further link to the interesting theories of Theo Venneman, who claims to have identified toponyms from Brittonic throughout Europe. There is a good deal of argument for how much Brittonic actually remians in English, and how much is stretching a point.
I forgot one piece. I alluded to it but did not elaborate; that is the theory that the idiosyncratic us of do and did in English is originally a Brittonic bit. Nice Germanic languages don't have this. Do you have any fish? Haben Sie keine Fische? There's nothing related to any "do" in that. I didn't make... Ich machen nicht... again, there is no "did" in it. In fact, not only do Germanic languages not have this, none of the 6000 languages of the world have this - except Welsh and Cornish, suggesting that some relative of those languages was able to keep that oddity in their speech despite being overrun by Germanic tribes who didn't have that. The theory is not universally accepted, but it's a good start.