The tune is called "Cranbrook", after a Kentish village (with an impressive windmill) and was composed by Thomas Clark as Folkie has already said. It was also used for the hymn "O for a Thousand Tongues to Sing".

Over the years the tune has been somewhat modified - by the addition of ascending repeats ("I saw thee" etc.) and also by raising a note (the "I" in the last "I saw thee") to make it easier to sing.

You can find a MIDI file of the original four part version of the melody HERE. Note that as in most music of the period the melody is held by the Tenor line not the Soprano (the word Tenor comes from the latin "To Hold").