Davies was born in Treorchy in the Rhondda Valley, Wales. His father, a clerk at a coalmine, died a few months later, and his mother took Donald and his twin sister back to her home town of Portsmouth, where he went to school.
He received a BSc degree in physics (1943) at Imperial College London, and then joined the war effort working as an assistant to Klaus Fuchs. on the nuclear weapons Tube Alloys project at Birmingham University. He then returned to Imperial taking a first class degree in mathematics (1947); he was also awarded the Lubbock memorial Prize as the outstanding mathematician of his year.
In 1955, he married Diane Burton; they had a daughter and two sons.
From 1947, he worked at the National Physical Laboratory where Alan Turing was designing the Automatic Computing Engine (ACE) computer. It is said that Davies spotted mistakes in Turing's seminal 1936 paper On Computable Numbers, much to Turing's annoyance. These were perhaps some of the first "programming" errors in existence, even if they were for a theoretical computer, the universal Turing machine. The ACE project was overambitious and foundered, leading to Turing's departure. Davies took the project over and concentrated on delivering the less ambitious Pilot ACE computer, which first worked in May 1950. A commercial spin-off, DEUCE was manufactured by English Electric Computers and became one of the best-selling machines of the 1950s.
Davies then worked for a while on applications such as traffic simulation and machine translation. In the early 1960s, he worked on Government technology initiatives designed to stimulate the British computer industry.
In 1966 he returned to the NPL at Teddington just outside London, where he headed and transformed its computing activity. He became interested in data communications following a visit to the Massachusetts Institute of Technology, where he saw that a significant problem with the new time-sharing computer systems was the cost of keeping a phone connection open for each user. He first presented his ideas on packet switching at a conference in Edinburgh on 5 August 1968.
In 1970, Davies helped build a packet switched network called the Mark I to serve the NPL in the UK. It was replaced with the Mark II in 1973, and remained in operation until 1986, influencing other research in the UK and Europe. Larry Roberts of the Advanced Research Projects Agency in the United States became aware of the idea, and built it into the ARPANET, which evolved into the Internet.
Davies relinquished his management responsibilities in 1979 to return to research. He became particularly interested in computer network security. He retired from the NPL in 1984, becoming a security consultant to the banking industry.