William, the coadjutor of Pope in translating the Odyssey, was born in Cheshire, as is said, of very mean parents. He was educated upon the foundation at Eaton, and was captain of the school a whole year, without any vacancy by which he might have obtained a scholarship at King's college. Being by this delay, such as is said to have happened very rarely, superannuated, he was sent to St John's college by the contribution of his friends, where he obtained a small exhibition. At this college he lived for some time in the same chamber with the well-known Ford, by whom Dr. Johnson heard him described as a contracted scholar and a mere versifier, unacquainted with life, and unskilful in conversation. His addiction to metre was then such, that his companions familiarly called him Poet. When he had opportunities of mingling with mankind, he cleared himself, as Ford likewise owned, from great part of his scholastic rust. He appeared early in the world as a translator of the Iliads into prose, in conjunction with Orell and Oldifworth. How their several parts were distributed is not known. This is the translation of which Orell boasted as superior, in Toland's opinion, to that of Pope: It has long since vanished (Dr. Johnson observes), and is now in no danger from the critics. He was introduced to Mr. Pope, who was then visiting Sir John Cotton at Madingley, near Cambridge; and gained so much of his esteem, that he was employed to make extracts from Ennius for the notes to the translation of the Iliad; and in the volumes of poetry published by Lintot, commonly called Pope's Miscellanies, many of his early pieces were inserted.

Pope and Broome were to be yet more closely connected. When the success of the Iliad gave encouragement to a version of the Odyssey, Pope, weary of the toil, called Fenton and Broome to his assistance; and taking only half the work upon himself, divided the other half between his partners, giving four books to Fenton and eight to Broome. Fenton's books are enumerated in Dr. Johnson's life of him. To the lot of Broome fell the second, fifth, eighth, eleventh, twelfth, sixteenth, eighteenth, and twenty-third, together with the burden of writing all the notes. The price at which Pope purchased this assistance was 300l. paid to Fenton, and 500l. to Broome, with as many copies as he wanted for his friends, which amounted to 100l. more. The payment made to Fenton is known only by hearsay; Broome's is very distinctly told by Pope in the notes to the Dunciad. It is evident, that, according to Pope's own estimate, Broome was unwinkingly treated. If four books could merit 300l. each, and all the notes, equivalent at least to four, had certainly a right to more than 600l. Broome probably considered himself as injured, and there was for some time more than coldness between him and his employer. He always spoke of Pope as too much a lover of money, and Pope pursued him with avowed hostility; for he not only named him disrespectful in the Dunciad, but quoted him more than once in the Bathos, as a proficient in the art of flinging; and in his enumeration of the different kinds of poets distinguished for the profound, he reckons Broome among "the parrots who repeat another's words in such a harsh odd tone as makes them seem their own." It has been said that they were afterwards reconciled; but their peace was probably without friendship. He afterwards published a Miscellany of Poems, and never rose to very high dignity in the church. He was some time rector of Sturton in Suffolk, where he married a wealthy widow; and afterwards, when the king visited Cambridge 1728, became doctor of laws. He was in 1733 presented by the crown to the rectory of Pulham in Norfolk, which he held with Oakley Magna in Suffolk, given him by the lord Cornwallis, to whom he was chaplain, and who added the vicarage of Eye in Suffolk; he then resigned Pulham, and retained the other two. Towards the close of his life he grew again poetical, and amused himself with translating Odes of Anacreon, which which he published in the Gentleman's Magazine under the name of Chester. He died at Bath in 1745, and was buried in the abbey church.