E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
You must go to Battersea to get your simples cut. A reproof to a simpleton, or one who makes a very foolish observation. The market gardeners of Battersea used to grow simples (medicinal herbs), and the London apothecaries went there to select or cut such as they wanted. (See NAVIGA.)