Doctor Who Restoration Team member and professional TV/film/multimedia composer Mark Ayres has a comprehensive history of how the original Doctor Who theme music was done.

There being no “synthesisers” [in 1963], the Workshop needed a source of electronic sound. They found this in a bank of twelve high-quality test tone generators, the usual function of which was to output various tones (square waves, sine waves) for passing through electronic circuits for testing gain, distortion and so on. They also had a couple of high-quality equalisers (again, test equipment – equalisers, or “tone controls”, were not that easy to come by at the time) and a few other gadgets including a “wobbulator” (a low frequency oscillator) and a white noise generator.