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. Thomas came on the good ship, Hector arriving Boston on July 26, 1637 or on an unnamed ship arriving with the Hector with his wife, Margery (Baker) Nash, and five children.
On Jun 4, 1639, he was an "after subscriber" to the Fundamental Agreement. He was commander of the ship, Charles sailing to London on June 21, 1679. Thomas was a gunsmith. His house was on the west side of State Street in New Haven, Connecticut.
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. 
Note: Genealogical Notes on the Founding of New England, page 245:
According to [William] Berry, Thomas Nash came from Bewdley in Worcestershire. (Gen. and Ped. of Hertfordshire Families, pp. 83?85.) He sailed with the Whitefield party arriving at Quinnipac or New Haven, in July, 1639, and was one of the signers of the agreement to remain together made on shipboard. Savage says he was of Guilford in 1639, but this is probably a mistake. (Steiner's History of Guilford, 1897, pp. 23, 29, 48.)
New Haven, Col. Rec., (I, p. 82) says: "brother Nash his shoppe did stand by the creeks." 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. 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.
His home lot was on the west side of State Street, about one-third distance from Chapel to Elm St. He was chosen a Fence Viewer "for Mr. Eatons & Mr. Davenports quarter", March, 1645?6. May 25, 1646, the General Court ordered: "In regard of severall occassions and worke to be done agaynst trayning day, bro: Nash is spared."
Before emigration, he was a member of the church in Leyden, Holland, and was on 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.