[3] Arbuthnott entered the Royal Navy in 1803 and served as a midshipman aboard the warship HMS Mars at the Battle of Trafalgar in 1805.

He was present at the capture of Le Rhin in 1806 and that of four French frigates off Rochefort by Sir Samuel Hood, 1st Baronet's Squadron in the same year.

[3] Sir Alexander was Grand Prior of the Sovereign and Illustrious Order of St John of Jerusalem, Anglia 1860–61.

[4] In 1827, Arbuthnott married in Kildare Catherine Maria ("Mary") Eustace (born about 1806 in Ireland; still alive in 1891 living in Sheepy Magna, Leicestershire), third daughter of Rev.

They had a daughter, Josette Eliza Jane Arbuthnot (born about 1829 in France; died 12 January 1909; married Major Frederick Wollaston).