Thanks all. Really helpful.
It was the chain line. Tried the tension first, but no luck. Even tried the chain super slack, but it was still noisy.
The front chain line was 47.5mm. The rear was at 65.0mm even though it looked fine by eye. Fortunately the Hope trials hub has plenty of spacers to get things just so.
Now running smoothly and silently. Will post some piccies later. Loving the simplicity of 1 gear, but so far still reaching for a ghost shifter with my right thumb at times!
In answer to some of the posts, the chain does have a quick link, which is now running silently. Not sure what the optimum chain pitch is for the White Industries front and Chris King rear, or if they even need the same pitch, but they both now seem quite happy with the 8 speed KMC chain.