During the war, he found the time to write his Ph.D. on relativistic cosmology, and gained his Ph.D. on Clock regraduations and general relativity as an external student of the University of London in 1943.

He wrote an influential book with Arthur Geoffrey Walker and HS Ruse entitled Harmonic Spaces in 1953.

He was elected vice president of the London Mathematical Society in 1977, a post he held for two years.

During that time, he was elected a member of The Royal Academies for Science and the Arts of Belgium.

Willmore retired from the University of Durham in 1984 after holding the position of Head of the Department of Mathematical Sciences on three separate occasions, covering most of his Professorship there.