The author plays with mains electricity.......
Not something I generally like doing, but the house appears to have healthy wiring., and no circuit breakers blew. After pricing new and rather plastic-y looking sewing machines, I decided to have another go at fixing the old one. I dismantled the pedal completely, found nothing obviously wrong, cleaned off all the gunk inside and put it back together. Plugged it in, switched it on, and no difference.
In the pedal, wired in parallel to the switch/rheostat there was also a Blue Mystery Component. I thought carefully about this Mystery Component, which, assuming all was well with the switch, was acting like a short circuit. In normal operation said Mystrey Component would have act like an insulator or something with a whopping high impedance. So after considering the safety aspects of playing with electricity - I took it out. Plugged the machine in and Yay! It Works.
The Blue Mystery Component turns out to be a baked capacitor wrapped in blue heatshrink. The baking and wrapping has rendered the value on the capacitor illegible, it looks like it could either be 8 or 12 uF. I would appreciate any guesses as to what its purpose was, and whether I am risking blowing up either the motor or setting the house on fire by simply leaving it out.
Suggestions as to the naming of the machine would also be appreciated, for those of you to whom the previous two paragraphs were complete gibberish.