Alexander Leith was related to the Earls of Kintore, of the Scottish peerage. He joined the Army as an Ensign on the 8th August 1792, promoted Lieutenant in October 1794 and on 27th November became Captain. Further promotions followed to Major, 1st August 1805, Lieutenant Colonel on the 7th February 1811; Colonel 19th July 1821; Major General 22nd July 1830; Lieutenant General 23rd November 1841 and General 20th June 1854. He was appointed Colonel, the 31st Regiment on the 14th June 1853.

Sir Alexander Leith served in Flanders with the 42nd Regiment, particularly at the defence of Nieuport. Served with 31st Foot at the attack of the post of the Vigie, and at the subsequent capture of St. Lucia, in 1796. In North Holland in 1799, and he was severely wounded and lost an eye at the battle of Alkmaar. In the Egyptian campaign of 1807, including the attack on Rosetta. He served afterwards in the Peninsula, from April 1812 to July 1814, and commanded the 31st at the battles of Vittoria, the Pyrenees on the 25th, 28th and 30th July, the Nivelle, the Nive, and St. Pierre (where he was severely wounded), storming the heights of Garris, battle of Orthes, action of Aire, and the battle of Toulouse. Sir Alexander received the Gold Cross and one Clasp.

During these years the 31st Foot were awarded further Battle Honours including Talavera, Albuhera, Vittoria and Nivelle.