Found the answer. It was inspired by finding this thread: http://www.tomshardware.co.uk/forum/259989-15-slowdown-nvidia-cards-minutes-play which suggests a temperature issue, or a problem with the cooling of the graphics card. Sure enough, the fan on the graphics card had got stuck and wasn't turning. Presumably the card was periodically overheating, slowing massively, then resuming processing once it cooled enough.
I was fortunately able to re-enable the fan, and the issue's gone away. Thanks to ChrisF for the suggestions and comments!