Hampson was born at 488 Audenshaw Road, Audenshaw, near to Manchester (now Tameside), and was educated at King George V School, a grammar school in Southport. His brother Eric was killed in a naval action during the Second World War. In April 2009 his sister Margaret was living in Preston.

In 1949, in collaboration with Christian vicar Rev. Marcus Morris, he devised a new children's magazine, the Eagle, which Morris took to the Hulton Press. In April the following year, a revised version of the Eagle hit the bookstalls. Its most popular strip was Hampson's Dan Dare, Pilot of the Future.

Like Alex Raymond and Milton Caniff in the U.S., Hampson instigated a studio system where, from his home in Epsom, Surrey, as many as four artists might work on two pages of the strip at any one time. When Hulton Press was bought up in 1959, and the Eagle moved to a new publisher, Hampson's studio system was disbanded due to its cost.

He drew The Road of Courage, a carefully researched and meticulously crafted telling of the life of Jesus, with the help of his longtime assistant, Joan Porter, which concluded at Easter 1961. Hampson then began to devise seven other strip cartoon ideas, which he intended to offer to the Eagle. Partly through his own mismanagement (he told no-one what he was doing) Longacre Press accused him of breach of contract. He was forced to resign, his new strips were impounded by the legal department, and he rarely drew for comics again. The remainder of Hampson's life was spent working as a freelance commercial artist for various publications including Ladybird Books.

Hampson was voted Prestigioso Maestro at an international convention of strip cartoon and animated film artists held at Lucca in Tuscany in 1975. A jury of his peers gave him a Yellow Kid Award and declared him to be the best writer and artist of strip cartoons since the end of the Second World War. In 1978 he graduated from the Open University. He celebrated by drawing a Dan Dare strip for the University's internal magazine. The punch line of the script involved the University getting an application from Dare's nemesis The Mekon.

In ailing health, Hampson died from a stroke and the lingering effects of throat cancer in July 1985, in Surrey, England.