Arms of Drury of Hawstead, Suffolk (junior branch): Argent, on a chief vert a cross tau between two mullets pierced or (Burke, Sir Bernard, The General Armory, London, 1884, p.302 "Drury of Thurston Rougham in Suffolk" (sic)). In fact the Tau Cross was not adopted by the Rougham branch (the senior branch) but by the junior Hawstead branch), see below).

The Tau Cross ( a symbol of Saint Anthony) was added to the Drury arms by a junior branch, albeit a prominent and numerous branch, of the family, namely by Nicholas Drury II (d.1456) of Saxham, who married Joan Heath. He was the second son of Sir Nicholas Drury I of Thurston, and the younger brother of Sir Roger Drury (d.1420) of Thurston and Rougham, MP for Suffolk, who married Margery Naunton (d.1405), da. and h. of Sir Thomas Naunton of Rougham (Brasses in Rougham Church). The descendants of Nicholas Drury II (d.1456) of Saxham, who thus also bore the Tau Cross were seated at Hawstead, Hedgerley, Riddlesworth, Bestorpe, Ickworth, Linsted, etc, and included the Drury Baronets (cr.1627). Thus the senior branch, seated at Rougham, did not adopt the Tau Cross. There is some confusion in the sources between Nicholas Drury I and his son Nicholas Drury II, with the Duchess of Cleveland stating that the Tau Cross was adopted by Nicholas Drury I, whom she says visited the Holy Land and fought under John of Gaunt (1340-1399) whilst Nicholas Drury II (d.1456), said by Blomfield to have added the Tau Cross, died 116 years after the birth of John of Gaunt and was thus too young to have fought under him.

Francis Blomefield, 'Hundred of Giltcross: Ridlesworth', in An Essay Towards A Topographical History of the County of Norfolk: Volume 1 (London, 1805), pp. 274-284. [1]:
Nicholas Drury of Saxham, the second son, went to the Holy Land, at which time he added the cross tau to his arms, which he ever after bore, as did all his descendants; he married Joan Heath of Mildenhall, by whom he had two sons, Henry Drury of Ickworth, Esq. his eldest son, and Roger Drury of Hausted in Suffolk, his second son

For early origins of Drury family see Cleveland, Duchess of, The Battle Abbey Roll with some Account of the Norman Lineages, 3 volumes, London, Vol.1, 1889, pp.345-9[2]:

The Drurys were first seated at Thurston in Suffolk, " at which Place Sir John (the son of the first who came over), John his son, Henry his grandson, and John his great-grandson, lived many years." Fourth in descent from this latter John were three brothers, Roger, Nicholas, and John, living in the latter half of the fourteenth century, from whom all the different branches of the family were derived. Sir Roger, the eldest, was the progenitor of the Drurys of Roughamj from Nicholas, the second, descended the Drurys of Ickworth, Hawstead, Besthorp, Riddlesworth, Egerley, &c. : and John was the ancestor of the Drurys of Wetherden, where he had his seat. Of these the most distinguished, as well as the most numerous, were the descendants of Nicholas. He it was who first added to his arms the Cross Tau ever after borne by him and all his posterity, in memory of a pilgrimage he made to the Holy Land (The Tau, or crutch of St. Anthony, was borne by the monks of his Order), after having fought under John of Gaunt in Spain. He left two sons : 1. Henry, of Ickworth, near Bury St. Edmunds, apparently in right of his grandmother, which was conveyed by his daughter Jane to Thomas Hervey in 1525, and is now the seat of her representative the Marquess of Bristol. 2. Sir Roger, of Hawstead, who died about 1495, and built a townhouse in Wych Street, called Drury Place, which gave its name to Drury Lane.