In the 1938 Directory, under the heading Parks and Recreation, section, Gardens. 3 gardens are mentioned, Hamilton Sq, Pearson Rd, Tranmere, Warrington St, Higher Tranmere.
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Hamilton Sq, no need of mention.
Warrington St Gardens are still there.
Pearson Rd Gardens?
The images below, directory, map 1888-1913, present day,1911 directory, 1950s.
It appears the houses on the left coming up from Argyle St South were built between 1902 & 1906, by 1911 they numbered 1 to 41, so the waste ground that's present on the modern day map couldn't have been the gardens in 1938, my initial thought.
God help us,
Don't send Jesus,
This is no place for children.