There's a possible marriage,July 1 1821,St.Leonard's Shoreditch=Mary Ann Williams,this is based purely on the birthplace of their eldest,assuming I've got the right Jonathan Lawrence occ:shoemaker married to a Mary Ann that is.
IGI pilot doesn't give any more details but Ancestry does have the marriage/banns listed but I don't have full access,maybe someone who has can take a look.
Unfortunately the IGI Walworth births start 1825.
You can put a link to this post on the Surrey board & see if anyone has the PR's.
My understanding is that the records are held at the London Metropolitan Archives.
jim