The British scientist who helped work out how to sequence DNA and paved the way for the modern revolution in the understanding of genetics, has died. Frederick Sanger, a biochemist who worked at the Medical Research Council's Laboratory of Molecular Biology in Cambridge until his retirement in 1983, was 95.

Sanger was awarded a share of the Nobel prize for chemistry in 1980 for his work on sequencing DNA. It was his second Nobel prize, having also won the chemistry award in 1958 for his pioneering work on the structure of the protein insulin. He is one of only four people to have won two Nobel prizes – the highest honours in science – and the only person to have won two Nobel prizes in chemistry.

Compared with his contemporaries, the discoverers of the structure of DNA, James Watson and Francis Crick, Sanger was a relatively unknown figure outside science. He never courted fame (describing himself as "a chap who messed about in his lab") and retired at the age of 65 to devote time to his garden. He even rejected a knighthood because, he told a journalist in 2000, he did not care to be called Sir. He was awarded the Order of Merit by the Queen in 1986.

Reading the DNA letters that make up genes of living organisms is done routinely in modern laboratories, and understanding how particular sequences influence a person's susceptibility to diseases such as cancer and heart disease is a major focus of medical research. Though Watson and Crick had worked out the structure of DNA's double helix in the early 1950s, and revealed that it held a linear code of base pairs (C, G, T and A), it took Sanger and his team at Cambridge to work out a way to read the DNA sequence. In the 1960s and 70s, Sanger developed techniques to clone the DNA of the genes under investigation and then add chemicals to break it into short pieces.

Sanger's group were the first to produce a whole genome sequence – 5,000 letters long of the virus phiX174 – and they also sequenced the first bit of human genetic material, the 16,000-letter sequence of DNA in a mitochondrion, the "batteries" inside biological cells.

Sanger was born in 1918 at Rendcomb in Gloucestershire. His father, a medical doctor, influenced his interest in biology. He graduated from the University of Cambridge in 1939, specialising in biochemistry. He was a conscientious objector and was allowed to continue with his PhD during the war. Over the next decade, he worked on the chemical structure of proteins and developed methods to determine the building blocks of the hormone insulin, something that had been thought impossible. That work led to the first of his Nobel prizes.

In 1962, he moved to the new Medical Research Council Laboratory of Molecular Biology along with leading scientists including Nobel laureates Max Perutz and Francis Crick and began working on the problem of sequencing DNA. His technique – "dideoxy" or "Sanger" sequencing – is still in use today to read DNA code, including the 3bn base pairs of the first ever complete human genome sequence published in 2003. The Wellcome Trust named the Sanger Centre after him, which is based in Cambridge and was the UK home of the international Human Genome Project.

Jeremy Farrar, director of the Wellcome Trust, said: "I am deeply saddened to learn of the death of Fred Sanger, one of the greatest scientists of any generation and the only Briton to have been honoured with two Nobel prizes. Fred can fairly be called the father of the genomic era: his work laid the foundations of humanity's ability to read and understand the genetic code, which has revolutionised biology and is today contributing to transformative improvements in healthcare. We are honoured that the Wellcome Trust Sanger Institute, which has done so much to develop our understanding of the genome and apply it to medicine, bears his name, and that the Wellcome Library holds his papers for posterity."

Colin Blakemore, professor of neuroscience and philosophy at the School of Advanced Study in London and former chief executive of the Medical Research Council, said: "The death of a great person usually provokes hyperbole, but it is impossible to exaggerate the impact of Fred Sanger's work on modern biomedical science. His invention of the two critical technical advances – for sequencing proteins and nucleic acids – opened up the fields of molecular biology, genetics and genomics. He remains the only person to have won two Nobel prizes in chemistry – recognising his unique contribution to the modern world."

Sanger married his wife, Margaret Joan Howe, in 1940, and had two sons, Robin and Peter, born in 1943 and 1946, and a daughter, Sally Joan, born in 1960.