If you are patient this website will eventually have indexed all the St. Paul Shadwell records from the C18th to the 1880s but it doesn't have the period you are interested in as yet.
http://www.parishregister.com/The IGI gives a potential baptism for John Thomas Bennett in Stepney
JOHN THOMAS BENNETT
Birth: 22 NOV 1830
Christening: 25 DEC 1830 Saint George In The East, Stepney, London,
Father: JOHN BENNETT
Mother: REBECCA
Other possibilities of siblings from the IGI in the East End of London area are
WILLIAM ROBERT BENNETT
Birth: JUL 1824
Christening: 27 JUL 1824 Saint Leonards, Shoreditch, London
Father: JOHN BENNETT
Mother: REBECCA
SAMUEL BENNETT
Birth: 01 JUL 1832
Christening: 01 AUG 1832 Saint Luke Old Street, Finsbury, London,
Father: JOHN BENNETT
Mother: REBECCA
JOSEPH BENNETT
Birth: 01 JUL 1832
Christening: 01 AUG 1832 Saint Luke Old Street, Finsbury, London,
Father: JOHN BENNETT
Mother: REBECCA
When did John Thomas Bennett emigrate?
What was his father's occupation?
Regards
Valda