The early British artifacts might not all be specificly Celtic (I have no knowledge about this one way or the other), but the language definitely is. There probably was another language spoken there as well before the Celtic took over, but we have no evidence on what that language might have been like AFAIK. The Romans did give Ireland the name Hibernia, but they didn't really go there as far as I know. It is not clear how the Irish Gaels came to Ireland, but they did go on to found Scotland later on. They were verifiably in Scotland around 400AD, but they might have been there earlier than that. The evidence on this is unclear, but they did a lot of sailing, and you can see the Irish coast from Scotland, so it's not that far.