There are a couple of possibilities on the IGI:
Charles Allen born 26/11/1815, baptised 07/07/1816 St. Martins, Birmingham. Parents James Allen and Mary
Charles Allen born 05/03/1816, baptised 10/06/1816, St. Pauls, Birmingham. Parents Thomas and Sussana
1841 Census:
St Pauls, Birmingham
Charles age 25 Brasscaster
Anna age 25
Emma age 2
Ann age 5