Stephen Farnum Peckham's 1922 elaborated the plausible theory that John Peckham was the same as Rev. John Peckham, son of Henry Peckham (d. 1616) of East Hampnett manor in Boxgrove, Sussex, England. This has been disproven; it is clear that Rev. John Peckham stayed in England through the 1640s and did not immigrate to Rhode Island in 1638.
Wrong surname "Crafts" for John Peckham's second wife
John Peckham's second wife, Eleanor, was incorrectly identified with the surname "Crafts" in a note from 1905 in The Boston Evening Transcript, naming as source SFP's 1903 article in NEHGR, even though SFP's article specifically stated that Eleanor's surname was unknown.
Conjectural Daughter Eleanor
On 8 May 1671, Eleanor Boomer, "was bound over to next court, a bond for her appearance being given in sum of £100, by John Peckham, Sr. and Nicholas Cottrell." This is the sole foundation for a later supposition in the Boomer family that Eleanor was the daughter of John Peckham.
Stephen Farnum Peckham, in his 1922 Peckham Genealogy (p. 213), described this supposition that John Peckham had a daughter Eleanor who married Matthew Boomer as "conjectures" and "mere straws." There is no known evidence, beyond this old supposition in the Boomer family, that Eleanor's maiden name was Peckham; and there is no evidence that John Peckham had a daughter named Eleanor.
John Peckham was born about 1610 in England. His parents are unknown.
John Peckham immigrated aboard The Griffin in 1634. John was admitted as an inhabitant of the Island of Aquidneck, Rhode Island, on 20 March 1638, which is the first known record of him in the New World.
John Peckham married firstly Mary Clarke on 20 May 1638 in Newport, Newport county, Rhode Island. Together they had the following children:
John became a freeman at Newport on 16 March 1641.
John married secondly Eleanor Weaver after 1648 in Newport, Newport county, Rhode Island.  Together they had the following children:
Rebecca (Peckham) Spooner;
Elizabeth (Peckham) Taylor;
Sarah (Peckham) Weeden;
Deborah (Peckham) Taylor;
Phoebe (Peckham) Gray.
A stone marked "I P" on the land of William F. Peckham in Middletown is supposed to mark the grave of John Peckham.
Charles Phelps Noyes, Noyes-Gilman ancestry, being a series of sketches, with a chart of the ancestors of Charles Phelps Noyes and Emily H. (Gilman) Noyes, his wife .., 1907.
Children of John and Mary (Clarke) Peckham
John, born about 1645; married Sarah ; had eleven children, and lived at Newport; died about 1712.
William, born about 1647; married (1) his cousin, daughter of Joseph Clarke; married (2)
Phoebe Weeden, daughter of William Weeden; was ordained the pastor of the Firs Baptist Church of Newport, Nov. 11, 171 1, probably after the death of his uncle, and died June 2, 1734. His wife, Phoebe, survived him.
CHILDREN OF John and Eleanor ( -) Peckham
Stephen, married, about 1682, Mary ; moved to Dartmouth, Mass., about 1686, and died there April 23, 1724.
Thomas, married (1) ; married (2) after 1683, Hannah (Weeden) Clarke, widow of William Clarke, son of Joseph Clarke, and sister of his half-brother William's wife; was deputy for Newport in 1708, and one of the proprietors of common lands. He died in 1709.
Clement, married Lydia ; was a weaver; lived at Newport, and owned lands at Tiverton; died in 1712.
James, probably unmarried; died at Newport, Feb. 26, 1712; left a large property, the inventory of his real estate in Little Compton alone amounting to ^644 9s. 6d. His sister Susanna, and her husband, I'eter Barker (31), signed among others as his legal representatives
On the next page of Noyes, follows:
Susanna, married (1) Peter Barker, son of James and Barbara (Duncan) Barker, who died probably in 1725; married (2) about 1730, Peter Wells (23), son of Peter and Wells of Kingston, R. I. (22); died after 1733.
Sarah, married probably John Greene, son of John and Mary (Jefferay) Greene.
Rebecca, married John Spooner, son of William and Elizabeth (Partridge) Spooner.
Deborah, married Robert Taylor, son of Robert and Mary (Hodges) Taylor.
Phoebe, born in 1666; married Thomas Gray, son of Edward and Dorothy (Lettice) Gray; died in 1746.
Elizabeth, married Peter Taylor, son of Robert and Mary (Hodges) Taylor, a brother of her sister Deborah's husband; died May 24, 1714.
From Charles Edward Banks:
John Peckham came from the parish of Woodnesborough, co. Kent, England. John Peckham was admitted an inhabitant of Newport after 1 May 1639. John Peckham of Nuport had his land in Newport recorded sometime between March 1641 and 16 March 1642. At that time he held 40 acres of land, 32 acres in a parcel near Hambrook Mill on Stony River, bordering land of Thomas Clarke, and the rest in meadow and his home lot. He appeared at a General Court of Election as a freeman on 16 March 1641. On 27 January 1642/3, John Peckum of Newport purchased land on the southeast corner of the town, next to his own land, from James Barker of Newport. In 1648, he was a full member of the First Baptist Church, and Eleanor Peckham (his second wife) was baptized that same year. He appears as a freeman of Newport in a list of freemen of the Colony made in 1655. John Peckham was taxed at Newport in 1680. He left a will, dated 6 January 1681, witnessed by John Clarke and Henry Tew, according to a list of seventeen wills presented to the Court in 1700 which lacked a third witness as required by law. However, the contents of the will are unknown.
From NEHGS Register
"John1 Peckham appears in Newport, R.I., in 1638. He was associated with the Clarkes and others, who were among the active supporters of Anne Hutchinson. His name is not found in any passenger list, nor in Boston records. It is probably that he came with the Hutchinson part on the "Griffin." He was a zealous Baptist, but his name does not appear on the list of those disarmed in Boston, nor among the followers of wheelwright, nor was he one of the signers of the Portsmouth covenant. He was a brother-in-law of John Clarke, and his lands were allotted along with those of William Freeborn, John Coggeshall and others who were the first settlers of the Island of Aquidneck in 1638, where, on May 20th, his name is in a list of those who were admitted inhabitants of Newport... A reference to his will is found in a list of seventeen wills (between 1676 and 1695) that were presented to the court in 1700... Soon after the first settlement of Rhode Island the Peckhams bought a tract of land one mile square in Little Compton, on which they build a house in 1640, which stood two hundred years and in which six generations of Peckhams were born... In a deed dated May 30, 1651, from Joshua Coggeshall and his mother Mary Coggeshall, to Walter Connigrave, the land is described as bounded "on land granted to Mary Clarke now deceased, sometime the wife of John Peckham." The grant referred to was made previous to 1644. Mary Clarke was the sister of the five brothers, Carew, Thomas, Jeremiah, John and Joseph and was born in 1607. It is not known where or when she was married or when she died. The date of his second marriage, the surname of his second wife, and the date of his death, are also unknown. There are reasons for believing that Mary Clarke was the mother of his sons John, Thomas and William.
From Newport Court Files
Wills were required to have three witnesses, so there is a court file that provides a list of early Newport wills with only two witnesses. One such will was that of John Peckham was recorded on 6 January 1681 and was witnessed by John Clark and Henry Tew.
It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: