The hormone research he became involved with in 1940 was initiated by the RAF who then believed German fighter pilots were given cortical hormones He remained a research Fellow at Oxford until 1948 working under Sir Robert Robinson, when he became the Smithson Fellow at the University of Cambridge where he remained until 1952. At Cambridge he worked with Lord Todd.
He returned to Australia in 1952 to take up a Professorship in organic chemistry at the University of Sydney, he was made a fellow of the Australian Academy of Science in 1954. He held his position at the University of Sydney until 1955 when he took a similar position at Manchester University. He was made a Fellow of the Royal Society in 1958.
Birch returned to Australia again in 1967 to establish the Research School of Chemistry at the Australian National University in Canberra, becoming its founding dean. He remained involved with the school until 1980. He served as President of the Royal Australian Chemical Institute from 1977 to 1978, and also chaired the 1977 Independent Inquiry into CSIRO.
He served as President of the Australian Academy of Science from 1982 to 1986. Birch was made a Companion of the Order of Australia (AC) in 1987 for his contributions to science in Australia. He was awarded Honorary Fellowship of the Royal Australian Chemical Institute, in 1994. He was also a founding member of the Australian Science and Technology Council.
Before his death in 1995, the Research School of Chemistry building at ANU was named the "Birch Building" in his honour.