In 1956, Woodward's work on radar information theory led Nobel Prize winning physicist John Hasbrouck Van Vleck to invite him to give a postgraduate course on random processes at Harvard University.

Professor Edwin Thompson Jaynes in his posthumously published book[8] recognized Woodward as having been "many years ahead of his time" and as having shown "prophetic insight into what was to come" in the application of probability and statistics to the recovery of data from noisy samples.

In June 2005, the Royal Academy of Engineering gave Woodward its first Lifetime Achievement Award, recognizing him as an outstanding pioneer of radar and for his work in precision mechanical horology.

From his experience as a mathematician and analyst of complex systems, he has made major contributions to scientific horology, including the definitive analysis of balance springs and much work on the properties of pendulums.

It was acclaimed by Jonathan Betts, the senior curator of horology at the Royal Observatory, Greenwich as "the nearest approach to perfection by any mechanical timekeeper not employing a vacuum chamber".

[13] He met his wife, mathematician Alice Mary Winter Robertson (1917-1999) whilst they shared an office in Durnford House in Langton Matravers as part of the Telecommunications Research Establishment.