Inglis was born in Casouli, India where his father, Lieutenant-Colonel John Eardley Inglis was serving in the 32nd (Cornwall) Regiment of Foot. His mother was the Hon. Julia Selina Thesiger, daughter of Frederic Thesiger, 1st Baron Chelmsford. By June 1857, when Inglis was less than a year old, his father was second-in-command under Sir Henry Lawrence at Lucknow where the British residency was under siege by Indian "rebels". Lawrence was killed during the early days of the siege, and as a result Col. Inglis took command of the British forces. Mrs. Inglis kept a diary of the events during the siege which lasted until November when the British were evacuated following the relief of the town by General Colin Campbell. Her diary was published in 1892.