Alfred Tadgell was educated at Wesley College, Melbourne, and completed his studies as an accountant. In 1882 he became accountant to the estate of the Clarke family (Sir William and his son Sir Rupert Clarke) retiring in 1937 at the age of seventy-two and after fifty-five years of service.

Tadgell's consuming passion beyond his formal work was botany, and he travelled extensively in Victoria, devoted to finding new plant specimens. He joined the Field Naturalists' Club on 9 February 1920, and was closely associated with the National Herbarium before that.

Tadgell wrote many papers, especially on Alpine Flora in the Victorian Naturalist, the journal of the Field Naturalists' Club of Victoria (FNVC). He collected thousands of Australian plants and corresponded with leading botanists in Australia, England and America. This collection and most of his botanical literature is housed at the National Herbarium in Melbourne.