Raised in Kent, England, Atkins came from a well-off family. Her mother passed away when she was young, so she was raised by her father, a respected scientist and the first president of the Royal Entomological Society of London. His position allowed Anna to step into science— women were restricted from the profession for most of the nineteenth century, although botany and botanical art were seen as an acceptable hobby. In her early twenties she produced several hundred scientifically accurate watercolor and graphite drawings of shells, to be published in her father's English translation of Genera of Shells (1822-24).

Atkins didn’t turn to photography until her early 40s. While she owned a camera, Atkins opted for the photogenic drawing technique—she learned the cyanotype printing method through its inventor, the astronomer and scientist Sir John Herschel, a family friend—to fashion her exquisite botanical images. She collected the sea specimens herself or from other amateur scientists, and made the plates by placing the wet algae directly on light-sensitized paper and exposing the paper to sunlight. To create the approximately fourteen copies of British Algae, she printed about six thousand cyanotype photogram exposures on hand-treated paper. The book was self-published without help from any enterprise or society. The resulting photograms are strikingly artful, the algae silhouettes seeming to float effortlessly, with gradations of blue showing in minute detail the varying shapes and density of the strands of seaweed.