Why is Peter Rabbit so popular in Japan?

My mother said “Wow, you have baby plates already!” on seeing our Peter Rabbit dinner service, but no, they were a wedding present from my wife’s family.

According to John Sergeant on Front Row a couple of weeks ago the illustrations were on ukiyoe, and the Lake District is what is traditionally considered beautiful scenery in Japan. Not entirely convinced by that, but all questions beginning with Why and all possible explanation are welcome on JapanExplained! Any more of either, anyone?