@ Artful Codger: Yes, Laura E Richards is the author (not editor/compiler) of everything in _In My Nursery_. Her name might have dropped off when tat poem entered school textbooks, though.

The World Cat listing above of the part-song, kindly provided by Guest 999 has the same J F Bridge as composer (though he seems to have gone by "Sir Frederick Bridge"). Here it is:

Named Person:        Laura E Richards
Document Type:        Musical Score
All Authors / Contributors: Frederick Bridge, Sir; Laura E Richards
Find more information about:   
OCLC Number:        223148916
Notes:        Caption title.
For chorus (ATTB) and piano.
Description:        1 score (7 p.) ; 27 cm.
Series Title:        Orpheus, no. 237.
Responsibility:        music composed by J. Frederick Bridge ; words written by Laura E. Richards.

But I am after the NON-part song form, which does exist in a collection, for I saw it with my own eyes.

Sanjay Sircar