Stuart had been tutor to King George III, and was from May 1762 to April 1763 his first appointment as prime minister.
On the death of Shallet Turner in 1762, the King preferred Brockett over Thomas Gray for the post of Regius Professor of Modern History at Cambridge University, a sinecure.
Brockett died on 12 July 1768 after a riding accident while returning from Hinchingbrooke, near Huntingdon, to Cambridge.
An ancient foliated cross in the porch of Gainford church, Co. Durham, is superinscribed as memorial to Lawrence Brockett, MA, BD of Trinity College, Cambridge.
There are several persons now living who retain a vivid recollection of the awful solemnity of the scene as the procession moved slowly on with its line of torches down the long and shady lane from Headlam to the last resting-place of the dead.