At the age of fourteen he was sent to University College School, of which Thomas Hewitt Key and Henry Malden had recently been appointed joint head-masters.

For several years he supported himself and others by private tuition, and after a time as an assistant master in his old school; and he acted as substitute for Henry Malden in the Greek chair at University College.

The college's early days were difficult, and in July 1857 Greenwood was appointed to the principalship on the resignation of Alexander John Scott.

[1] Within the next few years the scientific teaching of Sir Henry Roscoe and his colleagues improved the college's reputation; for his part Greenwood had an ally in Alfred Neild, who during most of his principalship presided over the governing body.

In 1867–71 a new chapter in the history of the college began with the movement for its extension, in which, with Thomas Ashton and others, Greenwood took a prominent part, leading to rebuilding on a new site and expansion.

Greenwood opposed the higher education of women on the same lines as that of men, and objected (at all events as a rule) to joint or mixed classes; but the new Victoria University had opened its degrees to all comers without distinction of gender.

Shortly afterwards he settled at Eastbourne, where he occupied himself with literary pursuits, including a revision of the text of William Wordsworth.