Your James was born in Hargrave, Suffolk in 1833 to James Peachey (b. 1794, c. 1800 Barrow, Suffolk) and Maria Jennison. James Peachey's was born to John Peachey (b. 1755/56 Mildenhall, Suffolk) and Esther Dearsley. John Peachey jnr's father was John Peachey (b.1730) but there were three of those in that area of Suffolk so then the trail goes cold. DNA is the only answer to get back beyond 1730.
My tree is on www.ancestry.com (peacheyford) or on www.genreunited.com