Constable's mother was Joyce Stafford, daughter of Sir Humphrey Stafford (1400 – 7 June 1450) of Grafton, Worcestershire, slain at Sevenoaks by the rebel, Jack Cade, and Eleanor Aylesbury (born c. 1406), the daughter of Sir Thomas Aylesbury (d. 9 September 1418) and his second wife, Katherine Pabenham (c. 1372 – 17 June 1436).

He fought at Flodden, where his father commanded the left wing, and was knighted 9 September 1513 after the battle by Thomas Howard, then Earl of Surrey.

[10] Constable served in the wars in Scotland in 1522 and 1523, and played a prominent part in the capture of both Jedburgh and Ferniehurst in September 1523, where his courage earned praise from Howard, by then Duke of Norfolk.

According to Bindoff, Constable was one of a number of Members, mainly politically conservative, who dined at the Queens Head to discuss parliamentary matters.

[10] In 1536 he remained loyal to the Crown when his elder brother, Sir Robert, became one of the leaders of the rebellion known as the Pilgrimage of Grace.