Etymology of brutish (and British)

Brutish
obs. form of British.
Oxford English Dictionary

brutish, a.
(ˈbruːtɪʃ)
Also 5–6 brutisshe, -ysshe, 7–8 bruitish.
[f. brute + -ish.]

1.1 Of or pertaining to the brutes, or lower animals, as opposed to man.
2.2 Pertaining to, resembling, or characteristic of the brutes:
a.2.a in want of intelligence or in failure to use reason: dull, irrational, uncultured, stupid.
b.2.b in want of control over the appetites and passions: passionate, sensual, furious.
†3.3 Rough, rude; savage, brutal. ? Obs.
†4.4 = brute a. 3. Of thunder: striking blindly, random. [after L. brutum fulmen.] Obs.
5.5 quasi-adv.
Oxford English Dictionary