Arms ("ancient") of Walsinghham "of Surrey" and of Scadbury Hall, Chislehurst, Kent: Gules bezantée, a cross couped chequy argent and azure. Arms of Sir Francis Walsingham (c.1532-1590) principal secretary to Queen Elizabeth I and popularly remembered as her "spymaster". As seen in 1562 stained-glass in East Window of Mereworth Church, Kent (Source:  C. R. Councer, Heraldic Painted Glass in the Church of St. Lawrence, Mereworth, Archaeologia Cantiana,  Vol.77, 1962, pp.48-62, esp. p.50 et seq[1]). 
Apparently the family's "ancient" coat of arms as two versions of the arms of "Walsingham of Surrey" are given in the Heraldic Visitations of Surrey for that family, in which is included 
w:Thomas Walsingham (died 1457) of Scadbury (Kent??), MP, husband of Margaret Bamme and Sir w:Edmund Walsingham (c. 1480–1550) of Scadbury, a soldier, Member of Parliament and Lieutenant of the Tower of London during the reign of King Henry VIII (uncle of Sir Francis Walsingham (c.1532–1590) principal secretary to Queen Elizabeth I and popularly remembered as her "spymaster"). The location of the Walsingham seat in Surry is not stated. 

The "modern" coat of Walsingham, quartered in the first quarter of a shield of 11 quarters, is: Paly of six argent and sable, a fess gules. As it is quartered first, this implies it is the "modern" coat of arms, with the "ancient" (i.e. superseded) arms of Gules bezantée, a cross couped chequy argent and azure shown in the second quarter. (Source: Pedigree of Walsingham family: Bannerman, W. B., ed., The Visitations of the County of Surrey made and taken in the years 1530 by Thomas Benolte, Clarenceux King of Arms; 1572 by Robert Cooke, Clarenceux King of Arms; and 1623 by Samuel Thompson, Windsor Herald, and Augustin Vincent, Rouge Croix Pursuivant, marshals and deputies to William Camden, Clarenceux King of Arms, Harleian Society, 1st ser. 43. London, 1899, pp.10-11[2])