The phrase to use one’s loaf means to use one’s common sense.

Here, loaf, a shortening of loaf of bread, is rhyming slang for head—cf. also to take the mickey out of someone and I should cocoa.

This use of loaf is first recorded in Soldier and Sailor Words and Phrases (London, 1925), by Edward Fraser and John Gibbons:

Loaf: Head, e.g., “Duck your loaf—i.e., keep your head below the parapet”. (Rhyming slang—loaf of bread).

The earliest instance of the phrase that I have found is from The Leeds Mercury (Leeds, Yorkshire) of Friday 26^th August 1938:

Our Witty Bricklayers
Rhyming slang still flourishes among bricklayers locally. I heard some of it in Pudsey recently from a foreman bricklayer, who assured me there was a rhyming slang word for almost everything in the building trade.
A bricklayer, for example, never asks his mate if he can borrow his pencil. He asks if he can borrow his York and Strensall¹. When he wants more bricks he asks his labourer to hand him up some King Dicks. If he wants halves (half bricks) he asks for cow’s calves.
When he admonishes an apprentice lad to use his head, he says:—“Use your loaf of bread, lad.” A board of mortar is always called a bullock’s slaughter, and a batten is called a Eugene Stratton (famous black faced comedian).
And if you can pronounce “joists” correctly, you will see why bricklayers always refer to them as “white mice.”

¹ Strensall: a village north of York.

On 14^th November 1941, The Hammond Times (Hammond, Indiana) published British Have Developed a Choice Brand of Slang to Describe Life in the Army, by Charles A. Smith:

London—Like their fathers in World War I, British soldiers in this war have developed a weird and wonderful brand of slang to emphasize and illustrate everyday army life.
Many of the slang words bear close resemblance to American slang, particularly of the Hollywood variety, but usually the British soldier manages to improve on the original with devastating effect.
The following is a list of publishable slang phrases now in current use by soldiers here with explanations of their meaning:
Bundook: Rifle.
Cheesed off, jarred off, or browned off: Fed up.
Chance your arm: Tantamount to trying it on.
Coming the old soldier: Same as chance your arm.
Duff: Pudding, pie, stewed fruit, cake, or anything in the nature of dessert for dinner.
Flog: To sell.
Gestapo: Military police.
Horrible man: Term of abuse, used scathingly by sergeants when addressing privates.
Hot: Usually accompanied by an unprintable adjective: meaning praiseworthy in the highest sense.
In the book: Named for the crime sheet².
Jankers: Confinement to barracks.
Kissem: Derivative of CSM., or company sergeant-major.
Muck: Any kind of dirt, from a speck of dust upwards.
Use your loaf: Derived from Cockney “rhyming slang,” in which the head is known as a “loaf of army pay.”
Golden eagle: Company paymaster.
Ruble: To become aware of.
To fluff a bloke: To see through him.
Get a rift on: Get a move on, sometimes accompanied by the old favorite “Get a jerk on.”
Slow as a stone slug: Member of the awkward squad³.
A steady: Perhaps the army’s most damning term of abuse: means a milk and water⁴, sweet as sugar type.
Umpty: Fed up.
Yellow bug: Deficient in stamina and or nerve.
Zipp: To get a move on.
Digger, spud hole, or mush: Guard room.
Tapes: Stripes (corporal’s, sergeant’s.)
Borrow: To take without the owner’s consent.

² crime sheet: a record of breaches of military regulations.

³ Charles James (died 1821), army officer and author, defined awkward squad in A New and Enlarged Military Dictionary, or, Alphabetical Explanation of Technical Terms (London, 1802):

Aukward Squad. The aukward squad consists not only of recruits at drill, but of formed soldiers that are ordered to exercise with them, in consequence of some irregularity under arms. This term has been likewise used, partly in ridicule, and partly in reproach, to mark out those officers who are negligent of their duty.

⁴a milk-and-water: a person lacking the will or ability to act effectively—cf. milquetoast.