1.  Sir John Bernard Burke.  1996.  "Burke's American Families with British Ancestry." Pages 2529-3022 from Burke's Genealogical and Heraldic History of the Landed Gentry (1939, Burke's Peerage, London).  Genealogical Publ. Co., Baltimore, MD.  On p. 2584:

BROWN formerly OF LAVENHAM... Edmund (Rev.), went to Plymouth, Massachusetts, 1638, Minister at Sudbury, Mass., 1640-78, bapt. at Lavenham, 28 Oct, 1606, matric. Emmanuel Coll., Camb., 1624; m. 29 Jun 1639, Anne, dau. of Anthony Whiting, of Dedham, and widow of John Lovering, of Watertown, Mass., and d. 22 June, 1678.

2.  Clarence Almon Torry.  1985.  New England Marriages Prior to 1700.  New England Historic Genealogical Society, Boston, MA (reprinted 1997, Genealogical Publ. Co., Baltimore, MD):

The locations are known residences of the husband, ending with the husband's place of death.  An entry in Torrey does not imply a marriage in New England; it only demonstrates the presence of a married couple there before 1700.  Torrey is a compilation of published sources, not primary records, so he should be considered a secondary source.
p. 105	BROWN, Edmund (-1678) & Ann (?BARNARD) LOVERINE, w John; aft 24 Nov 1638, 1644?, ?19 Jun 1639, no issue; Sudbury

3.  Charles Henry Pope.  1900.  The Pioneers of Massachusetts. C.H. Pope, Boston, MA (republ. 1965/98 by Genealogy Publ. Co., Baltimore, MD; Broderbund CD-504; online at Ancestry.com; Kindle e-copy sucks; ordered paperback copy from NEHGS):

p. 72

Rev. Edmund, came with Lechford, [see letter of L. to him, dated 10 (10) 1638, in Note-Book;] res. first at Plymouth. Rem. to Sudbury as minister; propr. 1639; frm. May 13, 1640. He d. 22 (4) 1678. [S.] Will dated 24 May, prob. 9 July, 1678, beq. to wife Anne; to his kinsman Samuel Goffe of Cambridge, whom he adopts as son and heir; to Harvard College £100, and to the town of Sudbury £50 towards a school, after death of wife; to kinsman John Browne of Bury St. Edmunds, co. Suff. Eng. and Thomas Reade of Sudbury; to man servant Richard Addams and maid servant Mary Plympton; to John Toll, James Whetcomb, Capt. John Greene and Thomas Walker.

If he came with Thomas LECHFORD, he arrived in Boston on 27 Jun 1638.

.  James Savage.  1860-62.  A Genealogical Dictionary of the First Settlers of New England Showing Three Generations of Those Who Came Before May, 1692.  4 vols.  Little, Brown, and Co., Boston, MA (online at Ancestry.com and GoogleBooks.com):

Vol. I, p. 23

EDMUND, first min. of Sudbury, came over 1637, freem. 13 May 1640, ord. in Aug. foll. d. 22 June 1677, had w. wh. had been wid. of John Lovering, as Barry says, but no ch.

.  Thomas Lechford.  1885.  Note-book kept by Thomas Lechford, Esq., lawyer, in Boston, Massachusetts Bay, from June 27, 1638 to July 29, 1641.  J. Wilson & Son, Cambridge (republished 1988 by Picton Press, Camden, ME).