He attended Eton College and went on to Christ Church University, Oxford.
He travelled overseas for two years after completing University and arrived in Queensland 1872. He set up buying various investments and by 1875 he was owner of Foulden Sugar Plantation in Mackay. Winning the seat of Bowen in 1875, Amhurst held the seat for two years before resigning in 1877.
Before his death, Amhurst had been in poor health.
Hoping a change would help him recuperate, he sailed on the Steamship Bokhara to head back to England but died at sea on the 3 January 1881.