Joseph Smith
born April 1837–April 1838
  in Preston, Lancashire
died very roughly 1907

NB that the Joseph Smiths born in:
the March quarter of 1838 in Chorley district (v. 21, p. 334)
the September quarter of 1838 in Preston district (v. 21, p. 509)
the September quarter of 1839 in Preston district (v. 21, p. 534)
are not this one (I have a copy of the birth certificates).

The christening of a Joseph Smith with parents of the right names at the church of St John, Preston on the 1 April 1838 is recorded by the LDS. This is the same church as the one where his siblings were christened, so seems very likely to be the right Joseph. Harry Jack has seen the record and says that it names Joseph as the "child of the late Joseph Smith, flax-dresser, and Jane, of Marsh Lane."

There are no Joseph Smith (or even 'J. Smith', ' Smith', 'Jos. Smith', etc.) births registered in Preston district between September quarter 1837 and June quarter 1838, but there are seven within the county of Lancashire.

1841 census: living with mother and siblings, and ?lodgers at ?Brigs Lane, Preston. Age is 2, born in county.

1851 census: living with mother and siblings at 30 Bow Lane, Preston. Occupation is Fisherman/Cotton Piecer. Age is 13 and place of birth is Preston.