I found this on the freebmd website It would seem he was registered with a different middle name.
Births Jun Qtr 1841
Surname First name(s) District Vol Page
Lancaster Robert Prout Booker St Geo East 2 101
you can use this information to order his birth record
I noticed in the 1841 census that there is a Harriet Brooks living with them at the Howards residence i wonder if this is any relation to the James Brooker who is listed in the 1851 census as a visitor roughly the same ages. hope this helps