I’d say that Uncle Sam is more of a symbol or personification of the US than a character. (Similarly for John Bull.) He’s not so much an iconic character as he is a literal icon.
US: Ronald MacDonald or Mickey Mouse
England (not UK): Robin Hood (…Harry Potter?)
France: Asterix The Gaul, The Count of Monte Christo
Spain: Don Quixote
Japan: Hello Kitty
Germany: Hansel and Gretel
Paddington hailed originally from darkest Peru, I believe.
The UK suffers from the same thing as the US - an awful lot of characters stretching back hundreds of years, all fairly well know to most on this english-speaking site.
Hamlet and Beowulf both hailed from Denmark (or maybe more precisely Sweden in Beowulf’s case), so does that mean that can’t be the most known British characters?
Winnie the Pooh for Canada? Although the author was British - the bear upon which the stories were based was from Canada, and named after the city of Winnipeg.
The bear upon whom the books was based was a teddy bear owned by Christopher Milne. He was named for Winnipeg the Bear, but she had nothing to do with the inspiration for the books, aside from providing the name for the toy.