Though my response may not directly help with your search, it could be a possible "relative"link.My Gx3 Grandfather, Henry BILLINGHURST, a bargeman and coal merchant, in Lewes (Cliffe), Sussex, had an accounts book that covered business dealings from 1831 to 1834. Within it, only one account is listed for a BILLINGHURST. It is very short with just two transactions: 1833 - January 1st - one-quarter chaldron* of coal, -January 15th - one-quarter chaldron of coal. The account is designated for a Miss BILLINGHURST of Cuckfield, Sussex. Henry was one of 5 children of Edward BILLINGHURST and Sarah EDWARDS. His siblings were Farncombe, Francis, John and William. The only info I have for William is that he was .. of Pulborough.
*chaldron -defn.: an English dry measure for coal and the like, varying in different localities from 32 to 36 or more bushels