Landin was born in Sheffield, where he attended King Edward VII School; he graduated from Clare College, Cambridge.

During the 1970s and 1980s, his efforts went into building the computer science department in Queen Mary College, developing courses, and teaching students, as set forth in the foreword to the textbook Programming from First Principles.

He is listed among those who attended the November 1959 conference in Paris,[6] and the 1962 conference,[7][8] and cited by Tony Hoare as one of the people who taught him ALGOL 60 and hence facilitated his expression of powerful recursive algorithms: "Around Easter 1961, a course on ALGOL 60 was offered in Brighton, England, with Peter Naur, Edsger W. Dijkstra, and Peter Landin as tutors.

Due credit must be paid to the genius of the designers of ALGOL 60 who included recursion in their language and enabled me to describe my invention so elegantly to the world.

The off-side rule allows bounding scope declaration by use of white spaces as seen in languages such as Miranda, Haskell, Python, and F# (using the light syntax).

[20] There is a Peter Landin Building at Queen Mary University of London housing teaching and research facilities for computer science.