1575 A "John Clarke the xxvjth of March" was baptized at St Mary, Rotherhithe, Surrey, England. 
1599/1600 A "Thomas son of John Clarke of Ratclif [was] baptised the viii day" at St Dunstan, Stepney, Middlesex, England. 
1600 A "Thomas Clarke the iiijth of Maye" was baptized at St Mary, Rotherhithe, Surrey, England. 
On an old version of his website, Caleb Johnson stated, [Caleb Johnson, MayflowerHistory.com http://www.mayflowerhistory.com/Genealogy/crew.php]
Master's Mate and Pilot of the Mayflower
John Clark was perhaps the John Clark baptized on 26 March 1575 in Rotherhithe, Surrey, England. He first went to Jamestown, Virginia in March 1610 as a ship's pilot. There, at Point Comfort, he was captured by the Spanish in June 1611. He was taken captive to Havana, Cuba, where he was interrogated, and then sent to Seville, Spain, and then on to Madrid in 1613. He was held as a prisoner until he was exchanged for a Spanish prisoner held by the English in 1616. He immediately went back to his occupation as a ship's pilot, and took a shipment of cattle to Jamestown, Virginia in 1619 under some-time pirate Thomas Jones. In 1620, he was hired to be the master's mate and pilot of the Mayflower, on its intended voyage to Northern Virginia. While the Pilgrims were exploring Cape Cod and Plymouth Harbor, the shallop was caught in a storm and Clark brought them safely ashore at an Island, which is to this day known as Clark's Island. After returning, John Clark decided to settle in Virginia himself. He went to Jamestown in 1623 on the ship Providence, with the intention of settling there, but died not too long after his arrival.
A more recent version states, 
Ship's Pilot and Master's Mate, John Clarke
John Clarke had been a ship's pilot on a voyage to Jamestown, Virginia in 1611, in the fleet that brought Sir Thomas Dale to govern the colony. He lived and worked ferrying cargo in the bay for about 40 days, until a Spanish ship came into the harbor. He was taken prisoner, tied up, and sailed first to Havana, Cuba, and later to Malaga, Spain, where he would be repeatedly interrogated by Spanish authorities. After five years imprisonment, he was released to the English in 1616. He took a load of cattle to Jamestown again in 1618, and was then hired for the Mayflower's voyage.
Coddington believed Thomas Clark to be the Thomas son of John Clarke of Ratcliff who was baptized at St. Dunstan's Church, Stepney, co. Middlesex, 8 March 1599/1600. Ratcliffe was and is a district in the large parish of Stepney, immediately on the north bank of the Thames, and inhabited almost exclusively by seafaring men. The parents of that Thomas were the John Clarke of Stepny & Mary Morton of St. Ellins, London who were married at St. Dunstan's Stepney, 19 Feb. 1598/9 ... "We believe, furthermore, that Thomas's father, John Clark or Clarke, was the Mate and Pilot of the Mayflower on her immortal voyage in 1620 ... [who] died at Jamestown, Virginia, in 1623." Anderson comments on this: "The hypothesis is very attractive, and was accepted by Jacobus [TAG 47:3], but remains underproven."
Glazier, ("John Clarke, Mate of the 'Mayflower' in 1620" by Prentiss Glazier, Sr.in Detroit Society for Genealogical Research Magazine, 47:42) however, says the TAG 42 article "erroneously assumed that the Mate had been the John Clarke of Ratcliff who married Mary Morton at St. Dunstan's in Stepney, Middlesex, in 1599, becoming parents of a son Thomas christened there 8 March 1599/1600, just eight weeks before the Rotherhithe Thomas Clarke. This mistake is understandable, since the churches are within sight of each other, just across the Thames from each other. It should be pointed out, however, that St. Dunstan's records (Memorials of Stepney Parish p. 199) show that 'Mr. John Clarke was chosen warden for Ratcliffe in 1627.' The mate had died in 1623. The error was unintentionally included in the 1973 Thomas Clark Family by Mr. and Mrs. Arthur H. Radasch."
Glazier cites Colonel Charles E. Banks, "Officers and Crew of the Mayflower," as placing him at Rotherhithe in Surrey, across the Thames River from Stepney on the outskirts of London. It was at Rotherhithe that Capt. Christopher Jones had moored his ship for several years, where four of his children were christened, and where he was buried in the churchyard. Others associated with the Mayflower -- part owners and crew -- were also of St. Mary's parish.
American Historical Review, cited by Banks, documents the capture of Mate John Clarke by the Spanish in 1611 just off the coast of Virginia and their two examinations of him: the first at Havana in 1611 and the second in Madrid in 1613.
Dr. Sturgis E. Leavitt adds details in his article "John Clarke before the Mayflower" in MQ 40:64-5. In the first interrogation, the Mate stated himself to be a native of London, 35 years of age, and of "the religion of the King"; in the second, he called himself an inhabitant of London, 40 years of age, and Roman Catholic. The reference to a large city as his home is understandable; the Spanish knew London but not the surrounding hamlets. His conversion (subsequently recanted) was probably a matter of expediency rather than doctrinal conviction.
Colonel Banks noted the age discrepancy and suggested "splitting the difference," approximating the birth year at 1574/5, a date easily reconciled with the 26 March 1575 baptismal entry at St. Mary's of Rotherhithe.... "Undaunted by the four years of imprisonment, the Mate made a second trip to Virginia in 1619, returning to join the Mayflower in 1620. In April 1623 he was back in Virginia, dying there soon after. Efforts to find his will, if any, have been unsuccessful."
It is possible that a will may yet be found, as seafarers frequently left a will before embarking on a voyage.
[From Evelyn Beran on Ancestry.com]
 London Metropolitan Archives, Saint Mary, Rotherhithe, Composite register: baptisms Aug 1556 - Nov 1630, marriages Jan 1555/6 - Nov 1630, burials Jul 1556 - Nov 1630, P71/MRY, Item 006, London, England, Baptisms, Marriages and Burials, 1538-1812, image 5, [AncestryImage].
 London Metropolitan Archives, St. Dunstan and All Saints, Stepney: Registers of Baptisms, September 1568–September 1608, P93/DUN/255, London, England, Baptisms, Marriages and Burials, 1538-1812, [AncestryImage].
 Donald Lines Jacobus, "Thomas Clark(e) of Plymouth and Boston in the Line of Nathaniel of Lyme, Connecticut," The American Genealogist 47 (1971), 3-16, at 4, [AmericanAncestors].
 London Metropolitan Archives, Saint Mary, Rotherhithe, Composite register: baptisms Aug 1556 - Nov 1630, marriages Jan 1555/6 - Nov 1630, burials Jul 1556 - Nov 1630, P71/MRY, Item 006, London, England, Baptisms, Marriages and Burials, 1538-1812, image 13, [AncestryImage].
 Caleb H. Johnson, MayflowerHistory.com, [Caleb_Johnson_Mayflower_History].