There is a biography for John Warren in Anderson's Winthrop Fleet along with several pages where his name is mentioned. The full citation would be:
Anderson, Robert Charles. The Winthrop Fleet of 1630. NEHGS, 2012. Pages 43. 312. 436. 661-665. 701, 703.
Pages 43 and 312 mention that John Warren came with three other men from the Nayland, Suffolk, England (versus Boxted).
Page 436 mentions John relevant to William Knopp (NOT KNAPP), whose son James Knopp married John Warren's youngest daughter Elizabeth Warren by 1655.
Pages 661-665 are a biography of John Warren (sometimes spelled Warrin). The first few pages provide information on land, service in the colony, etc. Page 664 provides a biography:
Baptized: Nayland 1 August 1585, son of John and Elizabeth (Scarlett) Warren [NEHGR 64:353].
Death: Watertown 13 December 1667, aged 81 [WaVR 1:29].
Marriage: By 1615 Margaret (Unknown). She died at Watertown on 6 November 1662 [WaVR 1:24].
Children:
1. MARY WARREN, bp. Nayland, Suffolk, 23 April 1615; bur. there 17 December 1622.
2. ELIZABETH WARREN, bp. Nayland 25 June 1618; bur. there 25 November 1622.
3. SARAH WARREN, bp. Nayland 20 April 1620; bur. there 7 September 1621.
4. JOHN WARREN, bp. Nayland 12 May 1622; m. Watertown 11 July 1667 Michal (Jennison) Bloise [WaVR 1:29]. widow of Richard Bloise and daughter of Robert and Grace (Unknown) Jennison [Dawes-Gates 1:369-71].
5. MARY WARREN, bp. Nayland 12 September 1624; m. Watertown 30 October 1642 John Bigelow [WaVR 1:9].
6. DANIEL WARREN, bp. Nayland 25 February 1626/7; m. Watertown 10 December 1650 Mary Barron [WaVR 1:9], daughter of Ellis Barron [TAG 20:135-36].
7. ELIZABETH WARREN, bp. Nayland 28 June 1629; m. by 1655 James Knopp, son of WILLIAM KNOPP {1630, Watertown} (eldest known child b. Watertown 21 April 1655 [WaVR 17).
There is a Bibliography Note that in 1910, Elizabeth French published English wills and parish register entries which identified the English origin of John Warren and three generations of his paternal ancestry [NEHGR 64:348-355]. Examination of the originals of the Nayland registers reveals only one discrepancy, in the baptismal date for the first daughter Elizabeth.
The most recent published accounts of John Warren and his family are by John B. Threlfall in 1990 [GMC50 479-93] and by Dean C. Smith and Melinde Lutz Sanborn in 1996 [Kempton Anc 1:463-91].
The remaining pages 701 and 703 show transcribed lists of names from the Winthrop Family Papers and the Group Listings of the immigrants.
I hope this helps.