The article that # kindly linked gives the history of the tune for "The Water is Wide." It was collected by Cecil Sharp.

It was whacky of Cecil Sharp to call the tune 'Waly, Waly' merely because a different song with the words 'waly, waly' in it shared many floating verses with 'The Water is Wide.' What WAS he smoking?

It's kind of like referring to the 'Wreck of the Old 97' as 'I Been Working on the Railroad' because they both have trains in them.

I know a nice 'Waly, Waly' that I learned from a CD by Martin Wyndham Read. The tune and words are different from 'The Water is Wide.'

When cockleshells turn silver bells
and mussels grow on ev-ry tree -
when blooms the rose 'mid frost and snows,
then will my false love prove true to me.
O, waly, waly, ah, love it is bonny

oops I've forgotten the rest!

It is a lovely song, well worth learning.