This is why I love AI. I remembered the story vaguely.
This is Saki's short story "The Toys of Peace" (H.H. Munro, 1914). It's not by Chesterton, Tolkien, or C.S. Lewis, but by the witty Edwardian satirist Saki, whose style has a similar ironic bite to Chesterton's.
The story matches your description almost exactly. It was inspired by a real 1914 campaign by the National Peace Council, which pushed toy manufacturers to produce "peace toys" (miniature civilians, civic buildings, tools of industry, and reformers) instead of toy soldiers and guns. The Council even staged an exhibit at the Children's Welfare Exhibition in London with a Peace Palace backdrop. Saki took that earnest idea and ran it straight into the ground with perfect comic timing.
The key scene
A well-meaning uncle (Harvey) brings his young nephews "the newest thing in toys" for Easter: a box of peace/civilian figures and models instead of the usual soldiers or siege toys their aunt had sent earlier.
He unpacks:
A square building he calls a "municipal dust-bin"
A lead figure of John Stuart Mill ("an authority on political economy")
A model of the Manchester branch of the Young Women's Christian Association
Robert Raikes (founder of Sunday schools)
A sanitary inspector, a district councillor, a ballot-box
A wheelbarrow, hoe, beehive, ventilator for sewers, school of art and public library
Mrs. Hemans (the poetess), Rowland Hill (penny postage), Sir John Herschel
The boys stare in silence. Then:
"Are we to play with these civilian figures?" asked Eric.
"Of course," said Harvey, "these are toys; they are meant to be played with."
"But how?"
Harvey gamely suggests they could stage a parliamentary election with the ballot-box. The boys immediately picture it with rotten eggs, free fights, and broken heads. Harvey retreats to the library to ponder writing a history book with no battles in it.
Left alone, the boys get to work. Within minutes they have repurposed everything for a lurid war game:
The municipal dust-bin becomes the principal fortified position in Manchester (they punch holes in it for cannon).
Robert Raikes is painted up as Louis XIV.
John Stuart Mill is dipped in red ink and becomes Marshal Saxe.
Mrs. Hemans doubles as Madame de Maintenon and then as one of the captured girls.
They launch a night invasion of Manchester, storm the YWCA, and slaughter a hundred girls (liberally splashing the remaining red ink across the building). Louis declares he has lost a marshal but "I do not go back empty-handed."
When the uncle returns and hears the carnage, he finds his sister and delivers the famous closing line:
"Eleanor," he said, "the experiment—
"Yes?"
"Has failed. We have begun too late."
About the "Britains" detail
Britains (W. Britain Ltd.) was the famous British maker of hollow-cast lead toy soldiers in exactly this period, so your memory has blended the real manufacturer of the war toys with Saki's fictional peace-toy set. There's no historical record of Britains actually producing a line of "toy pacifists," but the story's joke lands precisely because everyone knew what proper Britains-style lead figures were supposed to do: fight.
The boy's bewildered question—"but what does one DO with them?"—is the perfect distillation of the story's central gag. Normal children, given pacifist toys, will simply turn them into instruments of war. Human nature (and boy nature) is not so easily re-engineered by well-meaning adults with municipal dust-bins and John Stuart Mill figures.
The full story is short, public-domain, and widely available online (e.g., on Project Gutenberg or AmericanLiterature.com). It's one of Saki's best comic pieces and still lands perfectly more than a century later.
If you'd like the complete text, more context on the real Peace Council campaign, or help tracking down any contemporary illustrations or related pieces, just say the word.