My Willey ancestors were from Sheffield in the 18th and early 19th century; gg-grandfather William Willey moved to the east end of London to open a cutlery shop in about 1845. There are two Midland connections that I know of. William's brothers Henry and Charles both moved to Liverpool, but Charles's eldest son George (born 1840) went to Leicester. George's youngest child was a son, Walter, born in Leicester in 1890 (all his other children were daughters). George's younger brother Charles (born 1856) went to Cheltenham where he was living in 1901. Although married, i have no record of any children - they weren't there in the 1901 census. Neither Cheltenham no Leicester is particular close to Birmingham (both about 30 miles away) but at least this gives you some names to check ! If you do establish a link, please let me know and I can give you Willey ancestors back to about 1700.