See the COVE Master Map entry on Battersea:

https://editions.covecollective.org/place/battersea

In London Labour and the London Poor edition: 

Phase 1

Of the Street Sellers of Live Birds. (Volume 2): "The localities where these men "catch," are the neighbourhoods of the places I have mentioned as their residences, and at Holloway, Hampstead, Highgate, Finchley, Battersea, Blackheath, Putney, Mortlake, Chiswick, Richmond, Hampton, Kingston, Eltham, Carshalton, Streatham, the Tootings, Woodford, Epping, Snaresbrook, Walthamstow, Tottenham, Edmonton—wherever, in fine, are open fields, plains, or commons around the metropolis."

Phase 2

LONDON WATERMEN, LIGHTERMEN, AND STEAMBOAT-MEN. (Volume 3)