He was born in Glasgow on 28th November 1842, he was the only son of the Reverend George Thornton Mostyn, M.A., formerly incumbent of St Thomas’s, St Helens, Lancashire, and afterwards of St John’s, Kilburn, by his marriage with Charlotte, daughter of William Eccles of Glasgow.
He was educated at Rugby, and on 29th July 1862 he was gazetted as an Ensign in the 24th Regiment. He was promoted to the rank of Lieutenant on 23rd March 1866 and became Captain on 31st October 1871.
Captain Mostyn served with his Battalion at various stations in Great Britain and Ireland and in Burma, India, Gibraltar, Malta and the Cape of Good Hope, where from 2nd March 1878 - 6th July 1878 he acted as aide-de-camp to General Sir Arthur Cunynghame.
In November 1878 he proceeded with his Regiment to Natal to Natal to join the force which, with a view to the impending invasion of Zululand, which then being concentrated on the frontier. On 9th January 1879 his company marched from Pietermaritzburg to join the Head-Quarters which six weeks earlier, had left the capital, and formed part of Glyn’s Column at Helpmakaar. The company reached Isandhlwana on 21st January 1879. In the Battle which ensued on the 22nd January 1879, Captain Mostyn moved the men under his command out of camp to the support of another Company of his Battalion which, under Lieutenant Cavaye and 2nd Lieutenant Dyson, had engaged the enemy on a steep hill about 1,000 yards distant to the left. A few minutes after his arrival on the hill his Company extended and entered into action, supported on the right by a small body of native infantry. Shortly afterwards, the enemy appeared in great force in the rear, and the two Companies fell back slowly keeping up firing. After descending the hill which was rocky and precipitous, they formed in extended order at a distance of about 400 yards from it, but the enemy, heavily reinforced, pressed on rapidly and they continued to retire until within 300 yards of the position occupied by the Native Contingents. Shortly afterwards, the Zulus broke through the lines and Captain Mostyn and his men were overwhelmed.