The phrase Scout’s honour expresses the speaker’s good faith—synonyms: you can take my word for it, and honest Injun.

This phrase literally denotes the honour on which a Scout promises to obey the Scout Law, which was set forth by Robert Stephenson Smyth Baden-Powell (1857-1941), army officer and founder of the Boy Scouts and Girl Guides ¹, in Scouting for Boys: A Handbook for Instruction in Good Citizenship (London: Horace Cox, 1908):

THE SCOUT LAW.

I. A Scout’s Honour is to be Trusted.
If a scout says “On my honour it is so,” that means that it is so, just as if he had taken a most solemn oath.
Similarly, if a scout officer says to a scout, “I trust you on your honour to do this,” the scout is bound to carry out the order to the very best of his ability, and to let nothing interfere with his doing so.
If a scout were to break his honour by telling a lie, or by not carrying out an order exactly when trusted on his honour to do so, he would cease to be a scout, and must hand over his scout badge, and never be allowed to wear it again—he loses his life.

¹ The Girl Guides Association (now Girlguiding UK) was founded in 1910 as a counterpart to the Scouts Association.

Under the pseudonym of John Strange Winter, the English novelist and journalist Henrietta Eliza Vaughan Stannard (née Henrietta Eliza Vaughan Palmer – 1856-1911) mentioned the phrase on two occasions in her column What I Think, published in several British newspapers—for example in the Forres Elgin and Nairn Gazette, Northern Review and Advertiser (Forres, Moray, Scotland):

– Of Wednesday 28^th July 1909:

There are not many girl scouts yet. One of them belongs to me. She is leader of her patrol […]. I questioned something she said the other day, and she turned round upon me like a flash. “Scout’s honour, it is so,” she replied. There was nothing more to be said. Scout’s honour was good enough for me. And if scout’s honour is good enough for the hundreds and hundreds of young boys who consider that the most binding oath they can take, then let us have more of scout’s honour. […] All these boys, and I hope before long these girls, are being taught that there is something more than what Mrs. Grundy thinks, something more in the world than mere convention, that the expression “Scouts honour” is to them a solemn oath which no scout, whether boy or girl, would not die rather than break.

– Of Wednesday 20^th October 1909—the author writes about her daughter:

Our young scout was so impressed with the magnitude of her position that she immediately tried to instil her devoted family into a deep knowledge of reef knots, and hedge splice, and something to do with cloves. It is a great pity that she has not a dozen younger brothers and sisters to infect with her splendid enthusiasm. “Tired out?” she remarked to me one day. “Poor darling! Well, come and sit down on the big sofa and I will teach you how to make a clove hitch”—I think that was the phrase. However, I was not taking clove hitches, or any other refreshment of that kind. “He isn’t a bad little chap,” she remarked one day concerning a small scout of her acquaintance, “but he hasn’t the smallest notion of what ‘scout’s honour’ means.” You see, in this case ‘scout’s honour’ has come to be merely a parrot cry like many other good things—not to mention the bad ones.

The following extract from a letter published in the Aberdeen Press and Journal (Aberdeen, Aberdeenshire, Scotland) of Wednesday 29^th February 1928, indicates that children at that time already used the phrases Scout’s honour and Guide’s honour as pledges:

There are organisations […] which put a child on his or her mettle, apart from home or school discipline, so far as behaviour is concerned, and we hear youngsters clinching a statement, or sealing an undertaking, by quoting the words—“Guides’ Honour,” or “Scouts’ Honour.”

These, and other, pledges were later mentioned by the English folklorists Iona Opie (1923-2017) and Peter Opie (1918-1982) in The Lore and Language of Schoolchildren (Oxford University Press, 1959):

God and honour. Pledges such as the following are commonplace. ‘On my honour, ‘Honour bright’, ‘God’s honour’, ‘Scout’s honour’, ‘Crusader’s honour’ (or the honour of whoever is the hero of the moment), ‘Honest truth’ […].
[…]
[…] Scout’s, Cub’s ², Guide’s, and Brownie’s ³ honour, are the only pledges deliberately sown by adults to have taken root, and are sometimes accompanied by a left handshake, or by a salute with the appropriate number of fingers. A Birmingham girl who demanded ‘On your Girl Guide’s promise, and cut your throat if you lie’ seems, however, to have had doubts about the potency of the new pledge.

² The noun Cub designates a junior member of the Scout Association.
³ The noun Brownie designates a junior member of the Girl Guides Association.—Cf. origin of ‘Brownie’ and a hypothesis as to the origin of ‘brownie point’.

Victor Thompson used the phrase in two of his articles about the London Zoo, published in the Sunday Pictorial (London, England):

– Of Sunday 27^th January 1935:

When next I went to the London Zoo in search of material for this series a keeper in the Small Cat House informed me solemnly that his three Pandas had been up to mischief recently.
“Come, come!” I chided tolerantly. “I invent those never-never animals myself. I don’t believe in them.”
There Really Is Such An Animal
Not until I had seen the animals in question and tested their printed notices for invisible inks did I consent to believe that there really is a creature called the Panda. To-day I confess my past ignorance with shame, buoyed up only by the conviction that very few of you, either, could swear on your Scout’s honour that you had ever heard of the beast before.

– Of Sunday 19^th January 1936:

I this week have pleasure in introducing to you a strange animal called a river-hog, and I don’t mean a speed-boat driver.
Why strange? Because a river-hog has three tails, two of which, see that wet, grow from the tips of its long ears.
I speak on my Scout’s honour, but if you don’t believe me, look at the picture. Even with the nude eye, you can see that the ear ends in a wisp of coarse hair almost two feet long.
With two of these acting as lieutenants to its real tail, a river-hog can deal adequately even with the clouds of ravenous flies which live in its native Africa.

The following is from the Essex Chronicle (Chelmsford, Essex, England) of Friday 17^th October 1947:

All the big boys were at the boxing

Famous men, and men who hope to be famous one day, ducked into the ring at Chelmsford Corn Exchange on Tuesday and took a bow in front of another capacity crowd (writes Gilbert Saunders).
Shrewd, little silver-haired Ted Broadribb, former manager of Tommy Farr, introduced Britain’s light-heavyweight champion, Freddie Mills, and three up-and-coming youngsters from the Broadribb gymnasium.
Mills, in a dark blue suit that needed no padding and with his left thumb bandaged, promised “on his Scout’s honour” to give an exhibition as soon as the thumb was healed, in about four week’s [sic] time.

The phrase occurs in Rex North’s column, published in the Sunday Pictorial (London, England) of Sunday 24^th January 1954:

Dog’s disc
Scout’s honour, this is true.
Friend of mine called in a vet. to examine his dog. Diagnosis: “A slipped disc.”
A slipped disc, as you undoubtedly know, is the expensive name for lumbago when you are not on the National Health Service and paying large fees to the doctor.

K. John used the phrase in the review of The Quiet American (London: William Heinemann, 1955), by the English novelist Graham Greene (1904-1991), published in The Illustrated London News (London, England) of Saturday 14^th January 1956:

No one could dislike Pyle, the “quiet” American. This new-comer is a blushing schoolboy of thirty-two, cram full of idealism, and scout’s honour, and invincible ignorance.