Do you have any idea how old James was when he left England to go to Australia?
I found a family in the 1841 census that has Peter as the father and Mary as the mother with a bunch of children including a James who is age 3. Located in Romford, Essex.
If this is the correct James then he was a teenager when he went to Australia. Does this coincide with your information?
Also, what makes you think James was from Cheshire or Lancashire?