Sir Henry Neville's father was Sir Edward Neville (died 1538), of Addington Park in Kent, who married Eleanor, daughter of Andrew Windsor, 1st Baron Windsor, and Elizabeth, sister of Edward Blount, 2nd Baron Mountjoy.
His father was the younger brother of George Neville, 5th Baron Bergavenny and older brother to Sir Thomas Nevill, Speaker of the House of Commons.