The year 1745 was spent in a vague cruise in the Bay of Bengal, backwards and forwards from Ceylon to the mouths of the Ganges; and though two 50-gun ships, and , came out as a reinforcement, Deptford and one of the frigates were sent home with a convoy. For the time being the war was at a standstill; and a few weeks before a French squadron appeared on the station, Barnett died onboard Harwich at Fort St. David, Cuddalore, on 2 May 1746, after a few days' sickness. He had married, on 13 May 1725, Elizabeth, a daughter of Benjamin Rosewell, Esq., and had two surviving sons, Charles (1733–1811), later of Stratton Park, Biggleswade, and Benjamin (1735–1805), a banker, ancestor of the Barnetts of Glympton Park.
