He is the son of a builder of the same name who had fitted the sash windows and wainscot in the Senate House (1724-5), under James Gibbs, and had worked on the hall of Queens' College, Cambridge (1732-4).
[2] In 1760 he designed and built the new west range at Queens' College,[2] a white-brick building described by Nikolaus Pevsner as "impeccable of its kind but somewhat dull".
Over the next five years he restored the east front, and repaired the roof of the eastern limb of the church, together with the woodwork of the lantern, which neglect had brought to a dangerous condition.
The repairs executed between 1757 and 1762 were carried out conservatively, the old timber being, where possible, preserved; but Essex recommended the destruction of the west porch, as "neither ornamental nor useful".
[8] In 1760 he built the doctors' gallery in Great St Mary's Church (Burrough, architect), and the next year accepted a major commission at Lincoln Cathedral, where substantial repairs were needed.
Besides these he constructed an arch under the west tower, repaved the entire church, repaired the choir screen, and designed an altarpiece and bishop's throne.
At Ampthill Park, Bedfordshire he built the cross to commemorate Queen Catherine of Aragon, erected in 1773 for the Earl of Ossory.
[8] He was a close friend of Michael Tyson, Thomas Kerrich, Richard Gough, James Bentham, William Cole (whose house at Milton, Cambridge he built, and who made him his executor), Horace Walpole and other well-known antiquaries.
In 1756 he issued proposals for engraving views, plans, and sections of King's College Chapel; the scheme of this work, with plates drawn by his own hand, was among the manuscripts which, after his death, passed to Thomas Kerrich, who bequeathed them to the British Museum.
He was buried in St Botolph's churchyard, Cambridge, on the south side of the church, where a tomb commemorates him, his father, mother, wife, and children.
[8] Essex acknowledged the following works:[11] Besides these, his description of the old chapel of Sidney Sussex College, and his "Journal of a Tour through part of Flanders and France in August 1773", were printed after his death.