I see no one has mentioned this so I will -
The "James James" poem is "James James Morrison Morrison" I believe (James James Morrison Morrison Weatherbee George Dubree, took great care of his mother though he was only three")
The Chad Mitchell Trio recorded a setting of this poem ('way back in the vinyl days) perhaps on "Typical American Boys" perhaps not. I think the setting was Mitchell's, but not sure about that at all.
It's the only Milne piece I know of. (The Kenny Loggins tune is, I think "House at Pooh Corner")