Astbury was born in Longton, where his father was a potter. In 1916 he won a scholarship to Cambridge University, to study chemistry, physics, and mathematics, and graduated in 1921 after spending two years of the war doing x-ray work for the army. He then joined William Henry Bragg's brilliant group of crystallographers, first at University College, London, and from 1923 at the Royal Institution. In 1945 Astbury was appointed to the new chair of biomolecular structure at Leeds.

Astbury's early structural studies were carried out on tartaric acid but in 1926 Bragg asked him to prepare some x-ray photographs of fibers for his lectures. The results stimulated an interest in biological macromolecules that Astbury retained for the rest of his life. In 1928 he moved to the University of Leeds as lecturer in textile physics and by 1930 had produced an explanation of the extensibility of wool in terms of two keratin structures: α-keratin in which the polypeptides were hexagonally folded (unextended wool) and β-keratin in which the chain was drawn out in zigzag fashion. A popular account of this work was given in Fundamentals of Fibre Structure (1933).

The keratin structure established his reputation, and he quickly extended his studies to other fibers and proteins. He showed that the globular proteins consisted of three-dimensionally folded chains that could be denatured and drawn out into protein fibers. This work laid the foundation for the x-ray structural investigations of hemoglobin and myoglobin. The hexagonal α-keratin structure dominated British crystallographic protein studies until 1951, when it was shown to be incorrect by Linus Pauling who demonstrated the α-helical structure of polypeptide chains.

In 1935 Astbury began to study nucleic acids by x-ray crystallography, and in 1938 he and his research student Florence Bell produced the first hypothetical structure of DNA.