Bradford, Yorkshire, England Genealogy

I'm looking for information about a specific individual and his family & forebears. Thomas Clayton was born in Bradford, Yorkshire in about 1826, then moved to Australia before 1855. I can provide information about who he married (in Sydney, Australia) & his children. I know a fair bit about his wife and children, but almost nothing more about him. I do not know what boat he came to Australia on, when or where he died, when he was born (other than a reference on his marriage certificate which means he was born about 1826). He was born in Bradford according to a daughters birth certificate. I would like to know any of these above details, but most of all I'd like to find a record of his birth, and so get to records of his family in England (parents, grandparents etc). I have access to the records on [login to view URL], although have definitely not exhausted all there - the name is not all that unique, so potentially lots of leads to be chased down. Additionally I have barely looked at Bradford records. He may be a convict although I have no reason to believe so other than the era & that his wife was the daughter of convicts however. I'm happy to pay for results, and have several more UK deadends if you are good at your UK genealogy.