Armstrong was born in Rothbury, Northumberland, on 2 March 1970, the youngest of three children, to physician Henry Angus Armstrong and Emma Virginia Peronnet (née Thompson-McCausland). The Armstrongs are a North East landowning family distantly related to William Armstrong, 1st Baron Armstrong. Armstrong's maternal grandparents were economist Lucius Thompson-McCausland and Helen Laura McCausland (6 April 1903 – February 2000), granddaughter of Captain Conolly Thomas McCausland (13 May 1828 – 25 June 1902) and Hon. Laura St. John (12 June 1842 – 21 October 1919), daughter of St Andrew St John, 15th Baron St John of Bletso. The McCausland family held land at Drenagh.