Some of the "Kitty Alone" songs above seem to be versions of "Martin said to his man" rather than "Froggie went a courting".

The "Hey ho, say Rowley" version is "The Frog in the cock'd hat" which you can see on the Bodley Ballads website. The song has been around since November of 1580. It's ZN3249 in my broadside ballad index, and you can see the earliest known version on the SCA Minstrel website (in Mudcat's Links) in 'Melismata', 1611.

I counted up traditional texts of it Steve Roud's folksong index (Roud #16) and came up with 425. Some collectors published their texts in more than one place, so there aren't quite that many, but it appears to be one of the best known of folksongs in English. One most often can't tell what the chorus is from Steve Roud's entries, but one can see enough to know that the "Kitty alone" chorus isn't limited to American texts.