My Dad's Got a Gun From: Bob Bray told a version of this story at the Fleece. In And then it Happened by Ken Langsbury

Young Tommy's Dad didn't go to war.  Young Tommy says Our Mam wrote to them and said if they took Dad off to war there'd be nobody there to work the horse - and then they'd all starve.  And they had a letter back from Mr Churchill himself; said he didn't want the country to starve, so it would be best if Dad stayed at home and worked the horse.  The letter's there, on the mantelpiece, behind the clock.
Young Tommy didn't mind his Dad not going to war - because he couldn't abide fighting.  Not like some of them kids at school.  There was one of them last week, was stood up in the corner of the playground with all the little'uns sitting all around him.  "My Dad's got a gun!" says this lad.  "Cooorrr!" said all the little'uns, "Your Dad's got a gun!" "Yes - my Dad's got a gun!  He keeps it in a box with his medals." "Cooorrr!" said all the little'uns, "Your Dad's got a gun!  And he keeps it in his box with his medals."
"What's your Dad got, young Tommy?" "Nothing." And then young Tommy thought for a bit, and he says, "We got an old Army greatcoat." "Hoohooo!" said all the little'uns, "Young Tommy's Dad's got an old Army greatcoat!" "Got a brass button on it" says young Tommy.  "Cooorrr!  Young Tommy's Dad's got an old Army greatcoat, with a brass button on it." "Where's he keep it, young Tommy?" "He keeps it in the attic - over the tank," "Cooorrr!  Your Dad's got a tank ..."