According to the Victoria County History of Wiltshire:
Oatmeal Row takes its name from the market for oats and vegetables held near the Poultry Cross. Oatmeal Corner was mentioned in 14731
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[...] Oatmeal Row [...]
[...] know whether the use of the word ‘row‘ in the name of the many of these thoroughfares (Oatmeal Row, Butcher Row, Ox Row and Fish Row) is connected with their origins as ‘rows’ of stalls [...]