After succeeding to the business of John Almon in 1781, Debrett consolidated a position as one of the pre-eminent publishers and booksellers of the day. His shop in Piccadilly was said to be 'much frequented about the middle of the day by fashionable people... a lounging place for political and literary conversation' (John Feltham. The Picture of London. Phillips, 1802). In particular, his business was favoured by the supporters of the Whig party, and many of his publications catered to the sympathies of the Whig opposition. The supporters of the Ministerial party preferred Debrett's neighbour, John Stockdale.

Debrett was the publisher of two important early works on the beginnings of European settlement in Australia - Tench's Narrative of an Expedition to Botany Bay, and White's Journal of a Voyage to New South Wales. The journal of the First Fleet surgeon George Bouchier Worgan records that Tench, at least, has already made arrangements with Debrett for the publication of his Narrative before leaving England.