Born in Kensington, London, he was the oldest of eleven children of James Caer Greenwood, a coach builder, and his wife, Mary Ann, née Fish.

In its pages appeared the "sensation" novel Margaret Denzil's History, Greenwood's most ambitious work of fiction, also published in volume form in 1864.

The idea was taken up by George Smith, and the Pall Mall Gazette, named after Thackeray's fictional paper in Pendennis was launched in February 1865, with Greenwood as editor.

[5] Early in 1880 the Pall Mall changed owners, and the new proprietor, Henry Yates Thompson, shifted editorial policy to supporting the Liberal Party.

At the St James's Greenwood remained for over eight years, continuing to exercise a marked influence upon political affairs, notably as a pungent critic of the Gladstone administration (1880–1885) and an independent supporter of Lord Salisbury.

He continued to express his views on political and social questions in contributions to newspapers and magazines, writing frequently in the Westminster Gazette, the Pall Mall, Blackwood, the Cornhill, etc.

In 1905, on the occasion of his 75th birthday, a dinner was given in his honour by leading statesmen, journalists, and men of letters (with John Morley—who had succeeded him as editor of the Pall Mall—in the chair).