After her mother's death, she lived at Orford with her father John Blackburne, who was known for his interest in botany and his hothouses for exotic plants.

John Blackburne also had an extensive library where Anne probably studied botany; she later taught herself Latin so she could read the Systema Naturae of Carl Linnaeus.

Several species are named after Blackburne, including the beetle Geotrupes blackburnii, the Blackburnian warbler and the flowering plant Blackburnia pinnata, now called Zanthoxylum pinnatum.

[3][4][5][a][b] Her maternal grandfather was William Assheton, Rector of Prestwich, and the collector Ashton Lever, who established the Leverian Museum, was a cousin on her mother's side.

[15] They also owned merchant ships, were involved in trade with Russia, and produced salt in Cheshire that was then exported from Salthouse Dock in Liverpool.

[22] Blackburne did not contribute to botany and ornithology as an author in her own right, but she was widely known for the extensive and influential collection that she assembled, and she has been described as a "botanist".

[28][29] One of the naturalists who visited the Blackburnes was Johann Reinhold Forster, who in 1767 had been appointed as tutor in modern languages and natural history at Warrington Academy.

[31] In 1768, Forster dined at Orford Hall every Saturday, helped Blackburne with the arrangement of her insect collection, and read his lectures on entomology to her.

[4] Blackburne wrote a letter to the Swedish botanist and zoologist Carl Linnaeus on 29 June 1771, offering to send him "a few Birds & insects" collected by her brother Ashton near New York.

[10][46] Linnaeus's student Johan Christian Fabricius visited Orford Hall, where he examined her collection of insects, and found a new species of beetle.

[20] He later described the visit in his 1774 book, A Tour in Scotland, and Voyage to the Hebrides, where he praised John Blackburne's botanical collections and noted about Anna, "Mrs. Blackburne his daughter extends her researches still farther, and adds to her empire another kingdom; not content with the botanic, she causes North America to be explored for its animals, and has formed a museum from the other side of the Atlantic, as pleasing as it is instructive.

[50] In 1975, V. P. Wystrach determined that sixteen or seventeen of the bird species accepted by the American Ornithologists' Union were originally described by Pennant from specimens sent to Blackburne by her brother Ashton.

[51] Other than birds, Pennant acknowledged the Blackburne museum as the source for the descriptions of a mammal, a salamander, 3 species of fish, and 52 insects, also within Arctic Zoology.

[52] They exchanged mostly plants, preserved birds, and minerals, but also other animals, including a young musk deer that Blackburne obtained from Pallas in 1779.

[26][55] At some point between 1771 and 1779, Blackburne also became acquainted with the naturalist Joseph Banks, who also served as an intermediary between her and Pallas, and with botanist Daniel Solander as well.

[60][62][63] The Blackburne family homes at Orford, Fairfield and Hale Hall were all demolished in the 20th century, and the eventual fate of the collection is unknown; it was probably dispersed at auctions.