Hilton was born in London, and educated at St Paul's School. He won a scholarship to The Queen's College, Oxford in 1940.

During World War II, as an undergraduate, Hilton was obliged to enrol in training with the Royal Artillery, and was scheduled for conscription in Summer 1942. Instead, he was interviewed by a team touring universities looking for mathematicians with knowledge of German, and was offered a position in the Foreign Office without being told the nature of the work. The team was, in fact, recruiting on behalf of the Government Code and Cypher School. He accepted, and, aged 18, arrived at wartime codebreaking station Bletchley Park on 12 January 1942.

He was initially put to work on Naval Enigma in Hut 8. In late 1942, he transferred to work on German teleprinter ciphers. A special section known as the "Testery" had been formed in July 1942 to work on one such cipher, codenamed "Tunny", and Hilton was one of early members of the group. His role was to devise ways to deal with changes in Tunny, and to liaise with another section working on Tunny, the "Newmanry", which complemented the hand-methods of the Testery with specialised codebreaking machinery.

Hilton obtained his DPhil in 1949 from Oxford University under the supervision of John Henry Whitehead. His dissertation was titled, "Calculation of the Homotopy Groups of An2-polyhedra".

In 1958, he became the Mason Professor of Pure Mathematics at the University of Birmingham. He moved to the United States in 1962 to be Professor of Mathematics at Cornell University, a post he held until 1971. He was then appointed Louis D. Beaumont University Professor at Case Western Reserve University. In 1982, he was appointed Distinguished Professor of Mathematics at Binghamton University, becoming Emeritus in 2003. He now spends each spring semester as Distinguished Professor of Mathematics at the University of Central Florida.

Hilton constructed the 51-letter palindrome, "Doc note, I dissent. A fast never prevents a fatness. I diet on cod."