Final update for anyone who might happen to have the same issue:
I'm cautiously optimistic that this issue is now resolved.
Running the Latency Monitor software (thanks Vocalpoint) with no apps open, wifi disabled and AV switched off showed no problem initially, but if left for more than about half an hour would invariably show that my system wasn't up to the job of handling "real time audio". After looking at the performance monitor it looked like the CPU was running mostly at less than 2% but with the occasional large spike that would push it up to 80 or 90% of its capacity. Obviously some background stuff going on that couldn't be readily explained.
After talking with the manufacturer and digging around in various gaming forums it seemed that a common cause of CPU spikes like this, and the sort of CPU overruns that cause the pops, are outdated drivers, so I updated all the ones I could think of one by one, and checked with Latency Monitor each time.
The culprit appears to have been an outdated Nvidia graphics card driver

. Latency Monitor looks a lot healthier, and so far I've had no clicks.
Earlier in the thread I said that these clicks weren't visible in the waveform, turns out they are. I got lucky and caught one, so if anyone is interested in what the little buggers look like it's in the centre of this screen grab: