Let me clear up why i'm on about "Great Britain . . .
Folks can get burs under their saddles pretty quick around here. "Britons" can refer to persons who live in Great Britain or it can refer to the Celtic peoples of the British Isles (a.k.a. Brythons). From the context, it's clear you meant the first definition. Be assured that some of us actually understood that.
. . . to dispose of the snotty side seipe first, i understood that, too--but it doesn't alter that OP is abysmally ignorant of the ethnic make-up of the islands in 1066.
There are two divisions of Celts in those islands: the Brythonic Celts, comprised of the Welsh and Cornish (and the Bretons, who were more or less refugees from the islands); and the Goidelic Celts, comprised of the Irish, the Scots and the Manx. Even that doesn't cover it well. The Scots are called Scots because of the Irish colony of the Dalriada, whose inhabitanrs the Romans referred to as Scoti (at least as early as the 4th century). But at the time the Romans overran the island, the north of the island was also inhabited by Albans (largely in the western islands of Scotland) and Picts. The Picts likely came from Armorica, having been driven out by the Romans in the period of the Roman conquest of Gaul. I find it an unreasonable stretch to refer to the Welsh, the Cornish, the Manx, the Scots, the Picts and the Albans as Britons, as though it were some omnibus term for Celts--it is not.
As Joe has pointed out, William conquered England, not Britain.