I decided to pull apart my Quickie to paint the chassis plate as it looked out of place with my other gear.
After reassembly (and some cursing) I had this strange percussive sound coming through the left channel - a regular, quick electronic sound at something like 300 beats per minute (very rough estimate). Without knowing exactly why I thought this, I had a feeling that the sound was a capacitor discharging over and over, but I'm just saying that so you might get a sense of the sound - I don't know if that was actually the issue.
Swapping tubes made no difference so I took a look at the wiring and found that the earth connection between the 2 output RCAs had come adrift from the left socket. Resoldering the earth connection completely resolved the problem so hopefully this post will help others in future (assuming my description of the sound comes close to what others perceive).