Green’s Dictionary of Slang

box n.3

[abbr. SE colloq. brainbox]

the brain, the head.

[[US]C.H. Spurgeon John Ploughman’s Talk 159: If a man has not a soul above clodhopping he may expect to keep poor, but if he opens his sense-box, and picks up here a little and there a little, even Johnny Raw may yet improve].
implied in out of one’s box
[UK]K. Hudson Dict. of Teenage Revolution 26: Box. [...] With the meaning of ‘head,’ however – another purely British usage – the market for the word is much more restricted.
[UK]I. Welsh Trainspotting 87: The rush wastes nae time in racin tae ma box.

In phrases

out of one’s box (adj.)

1. (also off one’s box, out of the box) mad, eccentric, beyond emotional restraint; also attrib.

[US]L.W. Payne Jr ‘Word-List From East Alabama’ in DN III:iv 290: be off one’s base, (box, kerzip, nut), v. phr. To be out of one’s mind.
J. Neugeboren Big Man 143: ‘You’re out of your box,’ I say. ‘C’mon, c’mon,’ she says, ‘get your sneakers on, we got practice today, babes’.
NME 23 Dec. n.p.: He’s out of his box - refused to let Sid [Vicious] jam with him because he thinks Sid’s so appalling and it’s not worth talking about.
[UK]N. Barlay Curvy Lovebox 121: Bab’s out his box an’ he’s gonna do what he’s gonna do.
Online Sl. Dict. [Internet] out of the box adj 1. crazy, irrational. Note: theorized that the term is a vague allusion to the ‘jack-in-the-box’ toys, a box containing a head mounted on a spring that would pop open after a crank had been turned. The head would then bounce around. The unpredictable motion of the toy could be likened to someone who is ‘out of the box.’ (‘I don’t know what her problem is, but she’s completely out of the box!’).
[SA]Sun. Times (S. Afr.) Mag. 27 Jan. 10: I’m one for out-of-the-box thinking. I’m not a stereotypical artist.
[UK](con. 1980s) I. Welsh Skagboys 36: Ah’m ootay my box ranting about the brilliance ay the Minds’ Sons and Fascination album.

2. (also off one’s box, off one’s pot) completely intoxicated, whether by drink or drugs.

[UK]A. Sillitoe Start in Life (1979) 258: I thought she was right off her pot.
[US]Sounds 3 Mar. n.p.: They were stoned out of their boxes [KH].
[UK](con. 1950s–60s) in G. Tremlett Little Legs 143: Smoke one of those right through to the end and you were out of your box.
[UK]T. Blacker Fixx 205: Lolling about, stoned out of your box.
[UK]I. Welsh Trainspotting 49: Spud (drugs) and Second Prize (alcohol) were bombed out of their boxes.
[UK]Indep. on Sun. Culture 9 Jan. 4: Talking about how far out of their boxes they planned to spend the night (‘bit of cocaine, yeah. Bit of an e, yeah. Marijuana, yeah’).
[UK]N. Griffiths Grits 82: Eye fuckin right t’be scird, an all: av told yer, Colm’s off is fuckin box, mun.