The Phony King of England was a song featured in Robin Hood, and the song itself mocks Prince John, however it wasn't sung by Prince John. On the other hand, after this, the Sheriff of Nottingham and Sir Hiss are later heard singing the song until Prince John yells at them. 
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Little John: [singing] Oh, the world will sing of an English king 1,000 years from now, and not because he passed some laws or had that lofty brow. While bonny good King Richard leads the great crusade he's on, we'll all have to slave away for that good for nothin' John. Incredible as he is inept, whenever the history books are kept, they'll call him the Phony King of England.

Everybody: [singing] A pox on the phony king of England!

Little John: [singing] He stands alone on a giant throne, pretending he's the king; a little tyke who's rather like a puppet on a string. Then he throws an angry tantrum if he cannot have his way. Then he calls for mom, while he's suckin' his thumb. You see, he doesn't wanna play.

Little John: [singing] Too late to be known as John the first, he's sure to be known as John the worst, a pox on that phony king of England!

[musical interlude]

While he taxes us to pieces and he robs us of our bread, King Richard's crown keeps slippin' down around that pointed head. But while there is a merry man in Robin's wily pack, we'll find a way to make him pay and steal our money back. A minute before he knows we're there [speaking] old Rob'll snatch his underwear (everybody laughs) [singing] the breezy and uneasy king of England! That snivelin'- grovelin', measly- weaslin', blabberin'- jabberin', gibberin'- jabberin', plunderin'- plottin', wheelin- dealin, Prince John, that Phony king of England, Yeah!