Griffiths was born in Shropshire, England, but little is known of his early life; he began his career as a watchmaker at Stone, Staffordshire, before moving to London around 1741 to work for the Fleet Street bookseller Jacob Robinson.
He was an early campaigner for improving the literary status of female poets and novelists, and in a 1798 review of Elizabeth Moody's Poetic Trifles[5] wrote, the Age of ingenious and learned Ladies; who have excelled so much in the more elegant branches of literature, that we need not to hesitate in concluding that the long agitated dispute between the two sexes is at length determined; and that it is no longer a question, whether woman is or is not inferior to man in natural ability, or less capable of excelling in mental accomplishments.- New Series xxvii.
In 1750, together with his brother Fenton, he published John Cleland's scandalous Fanny Hill, or Memoirs of a Woman of Pleasure", which he had bought for £20, but which earned him a reputed £10,000.
[10] However, Griffiths ran into financial difficulties, and c. 1761 he was forced to sell a one-quarter share of The Monthly due to competition from the rival periodical The Critical Review.
Our booksellers, perhaps, write for but few, but the reason is that a multitude of our people trade more or less to London; and all that are bookishly disposed receive the reviews singly from their correspondents as they come out.