He was an original member of the Ivy Lane Club formed by Samuel Johnson in the winter of 1749, which met weekly at the King's Head inn.
Through the influence of Samuel Chandler he obtained the work of translating into Latin a number of tracts left by Daniel Williams, the founder of the library; but he tired of this task.
After a visit to France he resolved to translate François-Vincent Toussaint's Les Mœurs, but after the first sheets were printed stopped work Dyer's means at this time were very limited, his father having died and left the bulk of his property to his widow and eldest son and daughter.
Burke wrote the following notice of Dyer in one of the London papers: He was a man of profound and general erudition, and his sagacity and judgment were fully equal to the extent of his learning.
The modest simplicity and sweetness of his manners rendered his conversation as amiable as it was instructive, and endeared him to those few who had the happiness of knowing intimately that valuable and unostentatious man.Sir Joshua Reynolds and Malone both believed that Dyer was the author of Junius's Letters.
The evidence was of a weak and circumstantial kind: immediately after Dyer's death, Reynolds, who was one of his executors, entered his rooms in Castle Street, Leicester Square, and found William Burke destroying a large quantity of manuscript.