Not too difficult, and generally regarded as an engineer's party trick: all that it needed was a few lines of code to generate regular pulses somewhere, and a few more to select the frequency and duration of each note from a list. A speaker had to be hooked up for the purpose - with valves (vacuum tubes) there was enough power to drive a small one without further amplification.

I don't know about the Manchester computers, but some later ones had speakers fitted as standard, connected either to a dedicated output or to a selected part of the circuitry. Programmers and operators got to know the sound of normal operation (typically a hissy, rustling noise) and could tell immediately if a program got stuck in a loop or otherwise misbehaved.