Petersham is a village near London, in the modern borough of Richmond upon Thames. 

In London Labour and the London Poor edition: 

Phase 1

The Crippled Street-seller of Nutmeg-graters. (Volume 1): "My aunt, my mother’s sister, is married to a builder, in Petersham, near Richmond, and they are rich people—having some houses of their own besides a good business. I have got a boy to wheel me down on a barrow to them, and asked assistance of them, but they will have nothing to do with me. They won’t look at me for my affliction."