Note: I read the question this morning, then wrote my answer tonight. Somehow I came to think it included language and culture. It's now a bit of TMI, but I'm going to let it hang out there for a little bit because I worked on it for a few hours (sigh).
Their is some controversy surrounding the relation of Brittonic and Gaelic people. One theory says that they were both indigenous to islands, while the other says that Brittonic speakers came after 450 B.C. The Celtic language was originally discovered by Edward Lhuyd. He discerned a similarity in the two surviving Celtic languages, Gaelic (Irish) and Brittonic (Welsh). He became the first to propose that these were ancient languages that were spoken throughout Europe. He classified two families, of which Brittonic and Gaelic were the main members, into P-celtic and Q-celtic. He further proposed a Proto-Celtic substratum (not to be confused with P-Celtic). P-Celtic languages were also known as Gallo-Brittonic because they originated in Northern Gaul. They are also called Continental Celtic because they were mostly spoken on the continent. Q-Celtic has a more western, coastal distribution. It includes Goidelic (Irish-Gaelic), and Celtiberian (parts of Iberia). P Celtic is a younger, innovative branch of Celtic. Q Celtic represents and older, conservative culture, possibly dating from the Bronze or early Iron Age. This theory has taken the back seat in the last few decades, but has adherents.
The implication of this theory is that Brittonic people are related to Continental Celtic speakers, especially across the channel in Northwestern Gaul. There is evidence to support this. One point is the similar names of tribes on either side of the channel. I think that it had to do with the spread of La Tene culture into Britain. One theory says that they only entered the island in a significant numbers after 200 B.C. They also introduced coinage to the island from the continent c. 150 B.C. They pushed the previous Goidelic speakers out of Southern Britain.
In the 1970's a new theory emerged. This put Goidelic and Brittonic in a new category called Insular Celtic. It says that Brittonic and Goidelic developed together on the islands, and separated from each other at some point. The term Insular describes their isolation from Continental Celtic. Continental, therefore, would not be related to Brittonic, and would be completely extinct. The implication of this is that the both language groups are indigenous from a much earlier date, like the early Iron Age. The Insular Celtic theory has become the mainstream viewpoint, but their are proponents of the Gallo-Brittonic connection.
Goidelic is in fact related to the Celtiberian languages. This supports the older theory. It is also intriguing from the standpoint of Irish Legend. Irish Legends were compiled in the 12th century. In them, the eponymous ancestor of the Irish people was an Egyptian princess named Scota. She married a Babylonian and their son was Goidel Glas, the originator of the Goidelic languages. It describes the adventure his group of people who are called Milesians. They came from Asia, stopped in Iberia, then arrived in Ireland.
Ancient Irish people during the Roman period were called Scotti. Ireland was called Scotta. In a semi legendary reconstruction, they were the ancestors of the Scots. The Scotti created a kingdom called Dal Riata in the Western Scottish Isles, during the sixth century A.D. It contested with other people like the Angles and Vikings over the next centuries. Dal Riata imparted the Gaelic language and customs onto the Picts (who were a more savage people). It merged with them to create the Kingdom of Alba, c. 900. This was the predecessor to Medieval Scotland, which was a combination of this and Norman settlers.
Picts were described as foreigners by many people. They were often called Huns or Scythians. Their name is derived from the custom of painting their faces.
They formed a confederacy in the far north of Britain during the Romano British period. I think they may have previously been the enemies of Brittonic people. They originally spoke a distinct language called Pictish. They had a distinct form of art that was a fusion of of La Tene with later influences. They were viewed as the most archaic people of Britain, and this probably wasn't a maligned observation. Nobody knows where they came from.
What I haven't mentioned yet are the Brittonic speakers, which do not deserve to be last. Brittonic speakers were the primary subjects of Roman Britain, thus the name. After the Anglo Saxon invasions, the Brittonic speakers were represented by the Welsh, Cornish ("West Welsh"), and the Bretons. Cornwall was conquered by the Saxons at some point in the 10th century, and were assimilated. (Cornish identity was revived in the 20th century.) Wales was divided into a number of kingdoms which fought with eachother. The longest lasting one was the mountainous Kingdom of Gwynedd The Welsh seem to have held on to a remnant of Roman culture for a few centuries. They were a fiercely independent. They introduced the longbow to the English. They were eventually conquered in the 13th century, but most kept their identity and language.
Bretons were incorporated into France (Brittany) in the 15th century.