One of the mildest, most broad-minded and most cultured of scientists, Aaron Klug was once seen as a radical too dangerous to be permitted access to the US. The state department’s denial of his visa not only ensured he would make his research career in Britain, but also set the stage for his meeting with the X-ray crystallographer Rosalind Franklin that would define his scientific future.

Klug, who has died aged 92, won a Nobel prize in chemistry for his inventive approach to understanding how some of the key components of the living body assemble into its working parts. He was never a headline-grabber; his understated leadership of two of Britain’s foremost scientific institutions, the Medical Research Council’s (MRC) Laboratory of Molecular Biology (LMB) in Cambridge and the Royal Society, steered the scientific community’s response to major upheavals such as the Human Genome Project (HGP), the BSE crisis and the row over genetically modified food.

As a young South African with a Cambridge PhD, in 1952 Klug was on the point of taking up a post in the US. The South African government told the US authorities that his membership of a youth group meant that he was a communist. Offered the chance to “renounce” communism, he indignantly refused, never having taken it up in the first place. No visa being forthcoming, he returned to the UK.

From 1954, at Birkbeck College in London, he began to collaborate with Franklin on her studies of tobacco mosaic virus. They faced the immense challenge of solving the structure, not of a single molecule, but of the complex assemblies of proteins and nucleic acids that make up virus particles.

Franklin’s exquisite technical skill in producing X-ray diffraction images, combined with Klug’s deep theoretical understanding of matter, eventually enabled them to solve the general outline of the structure just before Franklin’s early death from cancer in 1958. He credited her not only with introducing him to viruses, but with showing him “that you have to tackle long and difficult problems rather than publishing clever papers”.

Klug’s fascination with assemblies of molecules and biological complexes led him to develop a new technique. Such assemblies fall in size between individual molecules that can be explored with X-ray crystallography, and structures that are large enough to see with a light microscope.

Electron microscopy covers this gap, but produces two-dimensional images that do not reveal detailed structural information. During the 1960s, working at the newly founded LMB, Klug showed how electron micrographs taken from different angles could be combined to reconstruct the whole structure in 3D. The inventors of X-ray CT scans later developed them from his methods.

He went on to use the technique to unravel complexes of protein and nucleic acid in viruses and in the chromosomes that carry genetic information. It was this work that brought him his Nobel prize in 1982, as the sole recipient.

In 1986 he was appointed the third head of the LMB, an institution that famously had “a Nobel fellow on every floor”. He was notably supportive of female colleagues, and of researchers with projects that were almost recklessly ambitious.

When the biologist John Sulston began to show that sequencing the whole genome of the nematode worm might be possible, he promoted him to head a new division of genome studies. He later negotiated with the MRC and the Wellcome Trust for Sulston to head the separate Sanger Centre (now the Wellcome Trust Sanger Institute), which successfully completed not only the worm genome but also one third of the international Human Genome Project.

Klug was knighted in 1988, and appointed to the Order of Merit in 1995. The same year he became president of the Royal Society, the UK’s premier scientific academy. On his watch it produced an authoritative report into bovine spongiform encephalopathy (BSE) and its transmission to humans.

This was the first of several that provided a basis for public discussion and policymaking. Responding to the GM food crisis of the late 90s, another report acknowledged that GM technology could not be deployed without winning the confidence of consumers. Klug recognised the importance of engagement between scientists and the public, and developed the Royal Society’s resources for working with the media.

Klug was born into a Yiddish-speaking family in Zelva, Lithuania, the second of two sons of Lazar, a cattle drover, and his wife, Bella (nee Silin). Lazar occasionally reported for newspapers in Kaunas, then the capital city. When Aaron was two years old and his brother Bennie four, the family migrated to Durban, South Africa, where Bella had relatives. After Bella died in 1932, her sister Rose took her place as the boys’ mother; in due course she married their father and had two more children.

This turbulent start to his life left Klug remarkably unscathed. A voracious reader, he breezed through Durban high school at the top of a class of boys two years older than himself (including his brother). After reading Microbe Hunters by Paul de Kruif, a classic work of popular medicine published in 1926, he decided to study medicine, and entered the University of Witwatersrand on a scholarship at the age of 15. In the same class was Sydney Brenner, also from a Lithuanian Jewish family, also 15, and also a future head of the LMB and Nobel prizewinner.

During his studies Krug’s interests shifted to pure science, and he graduated in physics, chemistry and biology. He followed this with a master’s degree in physics at the University of Cape Town. There his supervisor was Reginald James, who had survived Ernest Shackleton’s ill-fated Antarctic expedition in 1914-16. James was an X-ray crystallographer who had worked alongside one of the subject’s founders, Lawrence Bragg, at the University of Manchester.

Crystallography appealed strongly to Klug’s polymathic instincts, combining physics and chemistry and requiring both mathematical insight and experimental creativity to explore the atomic structure of molecules in three dimensions. It was at Cape Town, as he later recalled in his Nobel biography, that he developed “a strong interest ... in the structure of matter, and how it was organised.”

With James’s recommendation, Klug obtained an 1851 scholarship to go to the Cavendish Laboratory at Cambridge, now headed by Bragg, for his PhD. He arrived there in 1949 with his new wife, Liebe (nee Bobrow), a dancer and musician. He hoped to join the new MRC unit at the Cavendish, led by Max Perutz, which was exploring the structure of proteins. But Bragg assigned him to work on a theoretical project on how transitions occur in the microstructure of steel when it cools.

What many might have seen as a dead end, Klug approached as an opportunity: he later said that the work had assisted his thinking about the assembly of virus structures. He advised younger scientists to “equip yourself to do a wider range of things than you are actually interested in immediately. You never know what might pay off.”

The Klugs had two sons, Adam and David. As a family they retained a strong connection to their Jewish cultural roots, attending synagogue and observing festivals. They made many visits to Israel, being particularly attached to the city of Be’er-Sheva and Ben Gurion University, where a research centre is named in Klug’s honour.

Liebe and David survive him. Adam died in 2000.

• Aaron Klug, biophysicist, born 11 August 1926; died 20 November 2018

• This article was amended on 27 November 2018. Adam Klug, rather than his brother David, died in 2000.