George Alcock, immigrant to New England, was born about 1605.  Vol 1 P 17. 
The information regarding George’s matriculation at St. John’s College at Cambridge University further supports this birth date:
Alcock, George. Matric. Sizar from St. John’s Michs. 1622. One of these names went to New England In 1630: Deacon at Roxbury, Mass. (Felt, 160.)
As has often been remarked before, in order to understand the nature of collegiate life in Tudor England it is vital to understand how young they all were. When William Cecil lectured the Heads of House on the importance of keeping control of ‘inordinante youth’ he was not just thinking of the students, he was thinking of the Fellows as well. When Cecil had come to St John’s aged fourteen In 1535, his tutor, John Cheke, was just seven years his senior. The Senior Fellow in 1565, Richard Curteys, was barely thirty, having matriculated in 1550 at the typical age of about fifteen and become a Fellow at the age of eighteen. Over forty of his forty-eight colleagues had only joined the Fellowship in the reign of Elizabeth. Their average age was not much above twenty. The Master, Richard Longworth, was only thirty-three. 
From these two sources, one can learn that George Alcock matriculated at St. John’s College in 1622 and that the average age at matriculation is 15. Therefore we can conclude that George Alcock was most likely born during the first decade of the 17th century and not in 1581 as sometimes stated.
Considering the above information, it is likely that George Alcock married his first wife (Anne?) Hooker by about 1626. Having matriculated at the approximate age of 15 in 1622, he would have been about 19 in 1626. His eldest son John was baptized in January of 1626/7 according to GMB (Great Migration Begins)
George Alcock, page 17, Children: I. John: POB. St. Margaret’s, Leicester, Leicestershire, 21 January 1626[/7] (‘Johannes Filius Georgii Alcocke’).  Vol 1 P 2087.
He married second by 1637 in England, Elizabeth _____. She remarried after George's death April 1641 Dr. Henry Deengaine of Watertown, Dedham Roxbury and Boston.
Assuming that the information above is accurate, then we can eliminate most of the children attributed to George and Anne Hooker Alcock. Certainly John Alcock (b. 1604), Frances Alcock Hutchins (b. 1612), Ann Alcock Foster (b. 1617), And Sarah Alcock (b. 1621) are in error. Thomas Alcock (b. 1622 in Delaware) is unlikely because George and Anne didn’t arrive in The Colonies until 1630, and they were not in Delaware. George Alcock (b. 1624) can be eliminated also as having been born in The Colonies before his parents’ arrival.
The Rev. John Eliot records George’s death in the Roxbury Church Record as follows: He came in the first company in 1630 and left an only son in England. His wife died soon after his arrival. He was chosen Deacon of the combined Roxbury and Dorchester churches and after the Roxbury church was established he was Deacon of that church. He made two voyages to England and bought over his son, John, and a second wife by whom he had a son Samuel. He lived in a good Godly sort and died at the end of the 10 month 1640 and left a good Savour behind him, the poor of the church much bewailing his loss. Vol 97 P 11.
In addition, the will of George Alcock clearly states that he had two sons, John (b. 1626/7) by his first wife Anne, and Samuel, (b. 16 Apr 1637, Roxbury) by his second wife Elizabeth.
Therefore the only children correctly attributed to George Alcock were John and Samuel.
He immigrated in 1630 on one of the ships in the Winthrop fleet to Dorchester, Massachusetts, leaving his only son in England. His wife died during the first winter. He was made freeman May 18, 1631 and became a Deacon of the Dorchester church, but soon became member #51 of the new church at Rocksbrough (Roxbury), Massachusetts. He raised livestock and was a butcher . He made two return visits to England between 1630 and 1640, bringing back his son John and a second wife by whom he had his second son, Samuel.
22 Day 11th, called December, Anno Domini 1640.
The Last Will & Testament wch I George Alcock of Roxbury in N:E: doe make, havinge yet my perfect understandinge and memory according to the measure thereof.
Debts to be paid both In Owld England & In New
My debt of 40£ to my sonne John, wch I have of his in my hands. – Wife to have £100. To be paid her in whatsoever she shall chuse. – Brother Thomas Alcocke of Dedham all that he oweth me, & my heifer wch is wth calfe, wh came of the great cowe, If my goodes will howld out, else he shall have only hir calfe, & I give his 2 children each of them 2lb. – To our brother Edward Porter, 20 bushles of Indian Corne, & to our brother Chandler, the monye he oweth me. – To Elizabeth Blandfield 2l; she shall [be] put forth where she may be well educated. – to my servant Joseph Wise, my young heifer, & the rest of his time from after mid-Somer next. – To my servant, John Plimton, his time from after midsomer, for 5l. – My youngest sone shall have the silver bowles, & my wife the silver spoons. – My house and lands to be improved for the best, for the eaducation of my children, and the halfe of ye revenue of the farme shall be to eaducate my sone John in learninge, together wth the wisest improvement of his 40l. – The other half to educate sone Samuell, for 7 yeares, begining from ye 1st daye of ye 11 month, called January, about wch time expired, my sone John will be 21 years of age. – Part of the debts to my brother Carwithy be layde out on the 2 cowes I had of Mr. Perkins. – My loving brethren, Phillip Eliot, & William Park be my executors. My brother Mr. Hooker, Mr. Welde, Mr. Eliote, Isacke Heath to overseers.
Clearly George Alcock’s will mentions only two children, his sons John (who would be 21 in 1647) and Samuel. If the other children were truly his, he would have referenced them in his will since he leaves things to his brother and children, his brother-in-law, his two sons, a person of unknown relationship (Elizabeth Blandfield), a few servants, and a few “Brothers” in Christ.
Both the Moriarty article (“Alcocks of Roxbury”) and GMB state that there were two Alcock families that had children named George, Thomas, and Elizabeth. No relationship was found between these families.  Vol 1 P 18; 
It is possible that the two Georges were inadvertently taken as the same person and merged into one profile.
Birth: 25 Mar 1581 Cambridge, Cambridgeshire, England
↑ 1.01.11.21.31.4 Anderson, Robert Charles, The Great Migration Begins Immigrants To New England 1620-1633, New England Historic Genealogical Society, (Boston, 1995).
Gary Boyd Roberts, "#58 Royal Descents, Notable Kin, and Printed Sources: Elizabeth Boyd Roberts: A Genealogical Tribute, With 50 'New' Notable Kin of Stoughton, Scudder, Baldwin, Stanley, Martin (Bates-Stowe), Stebbins, Bullard, Hull, Latham (Dungan-Clarke), William Peck, Royce, Gaylord, Hale, Calkins, Cowles, Withington, Woodruff, or Alcock Descent;" Entry "46.: Cyrus Stephen Eaton," New England Historic Genealogical Society, Published: April 11, 2002
Trask, Mr. Wm. B., Abstracts of The Earliest Wills Upon Record in The County of Suffolk, MS, NEHGR (NEHGS, Boston, Mass., 1848) Vol. 2, Page 104.