From memory (and it is very singable):

The Rich Man Rides By

Mr William Shakespeare told us
Back in 1594
It's the rich what helps the rich
But it's the poor what helps the poor;
See the poor girl in the gutter
Morning, evening, afternoons,
Hear her stumble, see her stutter
'Won't you buy my air balloons?'

While the rich man rides by in his carr-I-age and pair.
What does he care? What does he care?
As the girl sells her airballs around London town
Crying 'eaven 'ellup me, I can't 'old them down'.
Up she flies straight to the 'evinly gate,
But there she can't stop,
Her airballs go pop;
She falls with a wallop in Lei-ces-ter Square
And the rich man rides by in his carriage and pair.

Verse is in 4/4. Chorus is in waltz time. Note that 'carriage' where it first occurs has three syllables. Americans will have no problem pronouncing 'Leicester 'with three syllables. That's the way all American visitors do it. But all of this - and the transposition of 'stumble' and 'stutter' in the verse - mark it out as a music hall song of the 1920s. It was recorded in 1926 by the seaside concert party artist Clarkson Rose on the Zonophone label as 'While the Rich Man Drives By' and reissued later on the cheap Ariel label. It has at least one other verse, but I can't find it in the BL catalogue or in Kilgarriff's great index.

This song has nothing to do (except in genre) with 'She Was Poor' or 'Won't You Buy my Pretty flowers';