The Online Historical Population Reports (OHPR) collection at www.histpop.org/ provides online access to the complete British population reports for Britain and Ireland from 1801 to 1937.
Searching for information on occupations in the 1870s in England and Wales I chanced across a report on the census of 1871 where in appendix A in Table 99, there's a list of "England and Wales occupations of the people arranged in alphabetical order" which includes numbers of people so employed.
Starting with Her Majesty the Queen, a unique occupation, the list, takes up 8 pages closely spaced, from accountant to Zinc manufacturer.
What is the first word in the second item in the image? There's just one woman who followed that occupation.
Other unique occupations were:
Designer of Fashions, Director of Nurses (Miss Nightingale's), Lithographic Stone Importer, Razor Strop Paste Maker, Steeple Jack, Vegetable Ornament Cutter.
Occupations, such as the mystery one above and the Steeple Jack entry are printed in italics indicating secondary occupations.