Hi John,
These are possible birth indexes for the children:
Eliza Sarah Parker march 1859 Pancras 1B 156
Sophia Parker December 1860 Pancras 1B 143
Death index for Sophia March 1865 Pancras 1B 12
From the IGI
Christening of Edwin Parker 26 December 1832 Marsh Gibbon Bucks
Parents Richard and Ann Parker.
If you go to the Family Search site:
http://www.familysearch.org/eng/Search/frameset_search.asp?PAGE=igi/search_IGI.aspput Parker in the last name box and put C109921 in the Batch No Box there are Parkers going back to 1598. In such a small village they are probably all related.
Bob