Fox studied mathematics as a scholar of Christ Church, Oxford graduating with a first in 1939 and continued to undertake research in the engineering department.

Fox's contributions were particularly notable because he combined practical skills with theoretical advances in relaxation methods,[3] which were to become important areas of research in numerical analysis.

The techniques applied to the computation of special functions had much wider applicability including interpolation, stability of recurrence relations and asymptotic behaviour.

During the 1950s, the group at the National Physics Laboratory worked on numerical linear algebra, which led to the publication of algorithms by Wilkinson and others.

Fox was also interested in the treatment of singularities in partial differential equations, the Stefan problem and other cases of free and moving boundaries.

He lectured widely on 'meaningless answers', describing some of the pitfalls of numerical computation from the uncritical use of simple methods Fox played a significant part in the early days of the Numerical Algorithms Group (NAG), which set out as a collaborative venture between Oxford, Nottingham and Manchester to provide a reliable and well-tested mathematical subroutine library.

At the National Physical Laboratory he was club tennis champion and captain of the cricket team, he also distinguished himself as a sprinter in the civil service championships.

[citation needed] Fox, who had enjoyed good health up to 1981, suffered from heart problems during his retirement and died from a ruptured aneurysm in the John Radcliffe Hospital, Oxford, in 1992.