The Salter English ancestry can only be definitely trace back two generations from Abigail Salter who married John Hammond in Watertown. Abigail's only known Salter ancestors are her parents and grandparents. There was a large Salter population in the county of Suffolk, England and it is possible that they are related to many of them, but how is not known.
Abigail's Salter grandparents were Thomas and Tomasin Joyner Salter. The birth dates of Thomas and Tomasine are unknown as are their birthplace. It is probably safe to say they were born in Suffolk, England by 1560. I have a working theory that Thomas' parents might be Roger and Margaret Salter of Buxhall. Roger was a shoemaker who owned houses in Buxhall and Great Finborough. They had a son Thomas who was baptized on 16 April 1559 at St. Mary's Buxhall. This would be right in line for a birth date by 1560.
Roger wrote his will in August of 1566 and it was proved the next year on 4 July 1567. Roger named in his will his wife Margaret who he directs to bring up his children who are:
1. George- who inherited the house in Great Finborough.
2. Thomas- who inherited the house in Buxhall
This is just a guess though.
thomas and tomasin
I do know that Thomas and Tomasin Joyner were married at All Saints in Semer, Suffolk on 20 October 1583. (only about 11 miles from Buxhall) Semer, today, is a tiny village and is classified as an Ancient Woodland. The couples first three children were baptized at All Saints, the parish church. They were:
1. Martha, bp. 10 October 1585, she married a man named Whitt. She was alive in 1648 and had four daughters.
2. George bp. 20 August 1587 (my ancestor)
3. Rose bp. 9 November 1588. nothing more is known.
Look at those three names; George, Rose and Martha. They are the names of Thomas' siblings. Coincidence? I don't know.
Thomas and his wife left Semer at some point and settled in Rattlesden, about nine miles to the north. Thomas had two further children. It is not know when or where they were born or if Tomasin was their mother. They were:
4. Elizabeth, b. 1590-1600, married John Sherman in 1619, she was dead in 1648, but had six living children named in her father's will.
5. Ann b. unknown, married in 1639. Ann was either a middle aged woman at the time of her marriage or she may have had a different mother than the rest of the Salter children.
Thomas Salter wrote his will on 25 March 1648. He was buried in the churchyard of St. Nicholas in Rattlesden on 3 April 1648. His will was proved in July. Thomas Salter's wife was buried in Rattlesden on 5 November 1646. It's a shame she died first, otherwise he might have named her in his will. Thomas did name his living children or his grandchildren if their parent was dead. Rose must have died unmarried or at least without children prior to 1648. Thomas left all his grandchildren £5 apiece. His youngest daughter Ann was given £20. A Jane Salter who married Anthony Skarp was named in the will, her relationship to Thomas is not known, perhaps she was a niece. 
Son George was sixty one years old when his father died it is possible that he had already taken over any land owned by Thomas.
george and elizabeth
George Salter married Elizabeth Munning on 29 October 1618 at St. Nicholas in Rattlesden. Elizabeth was the daughter of the Reverend Humprey Munning and Elizabeth Winthrop. Elizabeth was the daughter of William Winthrop, Uncle of Governor John Winthrop of the Massachusetts Bay Colony, making Elizabeth and John first cousins.
Their oldest son Thomas was born the next year, his baptism has not been found. All the rest of the children were baptized at St. Nicholas in Rattlesden. The image below, from the freereg website shows the marriage of George and Elizabeth and the baptisms of their children(green dots).
Not much is known about George and Elizabeth. He called himself a 'Grazier' in his will, which was proved in July of 1654. He and Elizabeth had moved to Dedham in Essex County by then. A grazier was someone who fattened cattle or sheep for market. Dedham was about 20 miles to the south of Rattlesden. In his will he leave bequeaths to his three children who are in New England, if they were still alive. Having already lost two children; Simon and Elizabeth, he knew full well that one or more of them might had passed away.
Elizabeth Munning Salter lived until 1660. She too wrote a will. Elizabeth knew by then that her two daughters had married in New England and named them Abigail Hammond and Hanna Phillips. It must have been difficult as a mother to say goodbye to the three children who left for New England, knowing that she would never see them again. Abigail Salter Hammond was my ancestor.
 "England, Births and Baptisms, 1538-1975, Transcriptions," database, Find My Past (findmypast.com : accessed 23 December 2016), baptsmal entry for Thomas Salter, 16 April 1559.
W. A. Coppinger, History of the Parish of Buxhall in the County of Suffolk, (London: London H. Sotheran & Co., 1902) 237, digital images, Archive (www.archive.org : accessed 23 December 2016).
"England, Boyd's Marriage Indexes, 1538-1850," database, Find My Past (findmypast.com : accessed 23 December 2016), marriage entry Thomas Salter and Tomasin Joiner.
 Leslie Mahler, "The Paternal Ancestry of Abigail (Salter) Hammond of Watertown and Hannah (Salter) Phillips of Boston," The New England Historic and Genealogical Register, Vol. 163 (April 2009) 113, digital images, American Ancestors (https:americanancestors.org : accessed 23 December 2016).
 Mahler, "The Paternal Ancestry of Abigail (Salter) Hammond."
 "Notes and Queries," The New England Historic and Genealogical Register, Vol. 55 (January 1901) 107.