Websites devoted to nursery rhymes frequently contain more misinformation than anything else, though that seems to come with the territory. The site linked to earlier presents all manner of discredited speculation as fact, and appears to identify no sources for anything. It should be treated with extreme caution, particularly as there is no evidence that the compilers have even consulted the standard work on the subject, ODNR. Perhaps they did but chose to ignore it, as it pours a good deal of cold water on many of the romantic and anachronistic fantasies so often associated with nursery rhymes in the popular imagination.

Back to our rhyme. Opie, Oxford Dictionary of Nursery Rhymes no. 322:

'A rhyme of strange fascination: many people have recalled the awe-inspiring effect it had on them when children, and yet how they continued to want it repeated to them. In Gammer Gurton's Garland (1784) the rhyme starts

A man of words and not of deeds
Is like a garden full of weeds.

This couplet in various forms appears to have been proverbial; it is found in several proverb collections, e.g. in James Howell's collection (1659), where is also included 'Good words without deeds are rushes without weeds'. Similar sentiments occur in Harley MS. 1927, of the time of James I, Harley MS. 6580, and Sloane MS. 406.'

Fletcher's use of the term 'deeds, not words' may indicate no more than an early recorded example of proverbial usage; or it may be no more than a coincidence. At any rate, we have no record of the rhyme itself until quite a bit later.

The Opies also quote the full text from Halliwell (though not his mysterious comments) and refer to 'a ball-bouncing song sent by a correspondent in 1946' and to other English examples recorded in the 1930s and '40s.

In the earlier thread, I quoted Roud number 2103 in relation to this; either I mis-typed the number or it has subsequently been re-classified. 2103 is actually 'The Other Side of Jordan' (though one entry under that heading, 'There was a man from Aberdeen', may just possibly be a form of our rhyme) and the correct number is 19103. The current Roud Index can be searched via the website of The Vaughan Williams Memorial Library:

Roud Folk Song Index.