I don't know of any Wandsworth connections.
Although some of our family left Coventry for Clerkenwell, London following their work in the watch and clock industry.
Are you in touch with Sheila Jelley? She knows more about the Jelley name than anyone else I've come across. She has a Family Tree attached to Ancestry.com so you will be able to find her.
My son Benjamin married a Geelong girl and emigrated to Geelong last November, Jelley reinforcements!