According to his friend Richard Polwhele, Hitchins when young worked as a miner, then went to Exeter to assist Benjamin Donn with his map (1765) of Devon; by 1761 he had contributed mathematical replies to The Ladies' Diary.
On 10 October 1763 Hitchins matriculated at Exeter College, Oxford; Polwhele says that the expenses of his university education were met by his wife.
In 1768 Hitchins became comparer, and in this capacity verified the calculations for the Nautical Almanack, work which he performed for the rest of his life.
While at Greenwich he entered holy orders, and moving to Exeter was for a short time vicar of Hennock.
The eldest, Richard Hawkins Hitchins (1764–1827), was a fellow of Exeter College, Oxford, and rector of Baverstock in Wiltshire.