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Born in Durban in 1920, Wadley attended Durban High School and then trained at Howard College (now of the University of Natal) in his hometown, where he studied under Hugh Clark and Eric Phillips. He was known as a student for his habit of rarely, if ever, taking notes in lectures due to his near-eidetic memory. During World War II, he was recruited into the Special Signal Services and trained on the British RADAR project.
After the war, Wadley joined South Africa's National Institute for Telecommunication Research as a designer of radio equipment and instrumentation. He developed an ionosonde for measuring Earth's ionosphere, and a ranging tellurometer. It was also here that he invented the Wadley Loop receiver, which allowed precision tuning over wide bands, a task that had previously required switching out multiple crystals. The Wadley Loop was first used in the Racal RA-17 a 1950s top of the range British military short wave receiver still considered one of the finest radio receivers ever made and later in the South African made commercially available "Barlow-Wadley XCR-30" radio. The Wadley Loop is more widely used today in spectrum analysers, where the noise sidebands of the analyser's tunable oscillator are cancelled since the spectrum analyser has to have sideband noise much lower than the signals being measured. The Wadley Loop effectively results in the noise of the spectrum analyser's band selection oscillator being cancelled so that the result equals that of the high Q crystal oscillator used to produce a "comb" of harmonics of the crystal ocillator frequency which is a fundamental feature of the design of the Loop.
He also invented the tellurometer, which could measure up to a distance of 80 km; it was used in land surveying. Today, it is used in a wide range of equipment but modified with current technology.
He was awarded the Frank P. Brown Medal in 1970. Durban High School instituted an annual mathematics prize in his honour in 2016.
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