I have Cox in Wandsworth from at least 1851, and James and Sidney are both common names in the family. If you find your line connects to the family shown below, I would be glad to share what I have.
[Since not often on this site, feel free to contact me by email: edited
1851 HO107/1578/F19
Frogmore, Wandsworth [Frogmore is the street name]
Thomas Cox/Head/Mar/43//Grocer & Baker/Hants Basingstoke//
Mary Cox/Wife///33//Essex Chigwell//
Celia Cox/Daug///10//Middlesex Kensington//
Alice Cox/Daug///7//Middlesex Kensington//
Edwin Cox/Son//5///Middlesex Kensington//
Jannett Cox/Daug///2//Surrey Wandsworth//
James W.Cox/Son//1///Surrey Wandsworth//
[Alfred 9, Edgar 7 elsewhere]
All the best, Roger