If the capacitor fails because it's shorted, the machine runs at full speed whatever the foot pedal setting. If the pedal works when you disconnect the capacitor, that confirms it's shorted. You can also test the capacitor with a meter, it should show a very high resistance if OK, or a low resistance if shorted.
You must be careful to get the right kind of capacitor. Don't get an electrolytic or tantalum type, they are for DC only, and will explode if used on AC.
I used a paper capacitor value 100nF, rated 300V AC, up to temperature 115 deg C.
100nF (nanoFarad) = 0.1uf (microFarad). 20% tolerance is good enough for this application. 10% is fine if that's all you can get.
Any voltage from 250V AC will be OK. That's the voltage it will stand without damage. So a 600V AC or 1000V AC will be fine if that's all you can get. If it's only got a DC rating, it needs to be 400V DC or more. (240V AC waveform peaks at over 350 volts).
The original capacitor, a YDK S-1 0.1uF, is cylindrical, with axial leads, ie leads to the centre of the circular ends. It's hard to find a capacitor of that shape nowadays. The one I used is rectangular, with leads coming out of the end corners. Just bend them to fit. You can re-use the glass fibre insulation sleeves from the old capacitor. Paper capacitors are not polarized, so it doesn't matter which way round you connect it.
I don't know what temperature, so I got one rated 115 deg C, but would have been happy with one rated at 100 deg C.
So, back to the original question, RS Components (rswww.com) have branches worldwide. Their description is "Kemet 100nF ±20% 250 V ac Paper Capacitor (Through Hole Mounting)", RS part number 311-1074, Kemet part number PME271YD6100MR30. Price 1.80 GBP for a pack of 5.
Oh, and yes it will work without a capacitor, which is there to stop the sparking as the wiper slides across the wires. Sparking causes oxidation and bad contact in the long term, so best to use a capacitor if possible.
Grandad Tom, January 2015