Thomas Nash, the "sonne of Thomas", was baptized March 27, 1589 at St. Leonard's Church in Bewdley, according to Gertrude Nash Locke in Lives & Times of the Nash Family, (Eaton Press, 1971, out of print). According to [William] Berry, Thomas Nash came from Bewdley in Worcestershire.
Before New Haven - Thomas Nash in Holland
Thomas Nash was among the Pilgrims in the church in exile, at Leiden, Holland, as evidenced by a letter from the Leiden church which he cosigned.
Journey to New England - 1639
Thomas Nash and his fellow immigrants sailed from London, about 20 May 1639, (ship name unknown), arriving with his wife, Margery (Baker) Nash, and their five children, in Quinnipiac Harbor (later known as New Haven Harbor) between July 6 and 10th, 1639.
Signed the Fundamental Agreement Jun 4, 1639
On the ship with the Nash Family was the Rev Henry Whitefield's party, who settled Guilford. On Jun 4, 1639, Thomas "Naish" was one of the signers to the Fundamental Agreement, pledging loyalty to each other and to be ruled by law of God, made aboard ship on the voyage to Quinnipiac.
A Gunsmith in New Haven
New Haven, Col. Rec., (I, p. 82) says: "brother Nash his shoppe did stand by the creeks." His house was on the west side of State Street in New Haven. He was a gunsmith, and probably well advanced in life at the time of the emigration, for his eldest son John was old enough to be made Freeman, April, 1642, and in his will of August 1st, 1657, he mentions his old age. He was chosen a Fence Viewer "for Mr. Eatons & Mr. Davenports quarter", March, 1645/6. The General Court ordered on May 25, 1646: "In regard of severall occassions and worke to be done agaynst trayning day, bro: Nash is spared." 
He was commander of the ship, Charles sailing to London on June 21, 1679.
Marriage and Children
Thomas Nash married Margery Baker, daughter of Nicholas Baker and Mary Hodgetts, in England before 1618.
Children of Thomas and Margery Nash (order is conjectural, based dates of marriage and births of their children):
Mary, born in England, married Roger Allen/Alling about 1643.
John, probably born about 1621; married Elizabeth Tapp; achieved military rank of major; lived in New Haven; served in various town offices for decades. 
Joseph, born before 1626; called sergeant; lived in Hartford, Connecticut; married Mary _____, then Margaret _____. (One of his wives may have had the maiden name of "Norton".)
Timothy, the youngest of the five children, was born in 1626 in England or Leiden, Holland; achieved rank of lieutenant; settled in Hadley, Massachusetts.
Margery died between 11 Feb 1655 and 1 Aug 1657; Thomas died 12 May 1658. 
Thomas is buried at Center Church on the Green Churchyard, New Haven, New Haven County, Connecticut, USA
Original Documents Establish Arrival in 1639
Mistaken date and ship: "Thomas came on the good ship, Hector arriving Boston on July 26, 1637...", as cited from Records of the Descendants of Thomas Nash of New Haven, Connecticut, 1640, compiled by Rev. Sylvester Nash, (1853) page 13. The date and ship Thomas Nash arrived on - Hector in 1637 - are supplanted and corrected by by research published in 1897.
In A history of the plantation of Menunkatuck and of the original town of Guilford, Connecticut : comprising the present towns of Guilford and Madison], (cited by R.C. Anderson), by Bernard Christian Steiner, (1897), page 24-26, letters and diaries of the times show Thomas Nash arriving on the unnamed ship at New Haven Harbor (not Boston) between the 6th and 10th of July, 1639.
The ship Hector did indeed arrive in 1637 at Boston -- only Thomas Nash was not on it.
Quinnipiac or New Haven
Note: New Haven was so named in 1640. When Thomas Nash arrived in 1639 it was still called Quinnipiac, as was the river which emptied into the harbor. The river is still called Quinnipiac, after the tribe of Indians who were endemic to that area before the arrival of Europeans.
Notes on Thomas Nash, by Earnest Flagg
Note: Genealogical Notes on the Founding of New England, page 245:
Savage says he was of Guilford in 1639, but this is probably a mistake. (Steiner's History of Guilford, 1897, pp. 23, 29, 48.)
The first date attached to his name at New Haven, is "1t of the 7th Moneth 1640", when he was admitted member of the General Court and received the charge of Freeman.
Before emigration, he was a member of the church in Leiden, Holland, and was one of five who wrote an interesting letter (given in full on pages 155, 156 & 157 of vol. 1 of the 4th Series of the Mass. Hist. Soc. Coll., 1852.) from there, Nov. 30, 1625, to their brethren in Plymouth, informing them of the death of John Robinson, Pastor of the church, which included in its membership the planters in Plymouth as well as those left.
↑ 1.01.1County genealogies, pedigrees of Hertfordshire families, page 83
↑ 2.02.12.22.32.4Genealogical Notes On the Founding of New England, 1629-1640 by Earnest Flagg, (1926), page 245
↑A history of the plantation of Menunkatuck and of the original town of Guilford, Connecticut : comprising the present towns of Guilford and Madison, by Bernard Christian Steiner, (1897), pages 24 - 26
New Haven, CT: Families of Ancient New Haven. (Online database. AmericanAncestors.org. New England Historic Genealogical Society, 2008.) Originally published as New Haven genealogical magazine. vols. I-VIII. Compiled by Donald Lines Jacobus. 8 vols. Rome, New York: Clarence D. Smith, 1923-1932. Vol 6, Page 1312 [cited by Anderson in The Great Migration Directory, page 237]
Ancestry.com. Genealogical Notes On the Founding of New England, 1629-1640, [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2007. Original data: Ernest Flagg. Genealogical Notes On the Founding of New England. My Ancestors Part in that Undertaking. Baltimore, Maryland: Reprinted for Clearfield Company, Inc. by Genealogical Publishing Co., Inc, 1990, 1996. Original copyright: 1926. Page 245, 309, 41, 50