Alexander was born at Croydon in Surrey, England in 1885, and was introduced to natural history by his two uncles, James and Albert Crosfield.
He moved to Australia in early 1912 to take up the position, which he held for three years before being made Keeper of Biology at the museum.
The project took him on visits to North and South America in search of a suitable insect agent and in 1924 he was promoted to Officer-in-charge.
The result of these overseas investigations was the highly successful use of Cactoblastis moths in controlling the Opuntia species in Australia and also arousing his interest in oceanic birds.
So when he left Australia in 1926 he spent most of the year at the American Museum of Natural History preparing the book Birds of the Ocean (1928), a forerunner of later field guides, before returning to England.