Born in London, he studied experimental psychology in Cambridge and later joined Acorn Computers.
Johnson-Davies contributed articles to Acorn User and created Identifont, a website that identifies typefaces from samples.
In 1980, Johnson-Davies completed a PhD and then went on to join Acorn Computers, developers of the BBC Micro.
Johnson-Davies was the founder and managing director of Acornsoft, publisher of video games such as Elite and the View business software range by Mark Colton.
In the October 1986 issue, he wrote "Spider Power" alongside quantum computing pioneer David Deutsch.