Reeve was born in London, the only child of well-to-do parents who died when he was around five years of age, and he was placed under the guardianship of a grandfather, who appears to have been a bit of a tyrant.

He joined a professional company under the usual conditions for an aspiring actor in those days — no pay and provide your own wardrobe — and was given bit parts.

Reeve unfortunately forgot his lines, and thenceforth was reduced to walk-on non-speaking parts, with no prospect of advancement, so the aspiring "Hamlet" and "Young Norval" left and found another manager, in Whitehaven, Cumberland, under the same terms — nothing a week and find your own wardrobe.

In 1852,[3] in Plymouth, as the outcome of a bet, Reeve wrote a farce, An Australian Hoax which, to win the wager, he had in production within a week and on the stage in ten days.

He gave as his opinion that the public should support second-tier pieces by up-and-coming companies as well as the "hit shows", as only then could theatre progress.

He also expressed the hope that Adelaide and the State would flourish under what to him would be the wisest and greatest advance in the history of Australia — Federation of the Colonies.

Apart from his early farces, An Australian Hoax and Supper Gratis mentioned above, Reeve was author of the comedies Only Dust,[10] Never Count Your Chickens, Parted, The Better Angel, I Have You, Won at Last, Not So Bad After All, Pike O'Callaghan and Obliging a Friend and dramatized Mrs. Riddell's George Geith[11] and, with the acquiescence of Wilkie Collins, Great Temptation, his adaptation of No Name.

In a farewell speech, Sir Samuel Way said the society had been exceedingly fortunate in having had for so many years the services and advice of a man of such high culture, who had made a lifelong study of Shakespeare's works.

He was a popular lecturer on subjects dear to his heart, and frequently preached from the pulpit of the Unitarian Church on Wakefield Street, Adelaide.

Reeve was the first captain of the Corps of Commissionaires, a body of the citizens' militia in Adelaide, and as with the Theatre Royal, was succeeded by Pollock.