Prolific TiVo Community member CWaring has revealed how TiVo behaves when it's web connection isn't working properly.
What became apparent was that TiVo doesn't appear to cache data locally! The pictures don't appear, and the "programme details" page can't even load at all.
We're grateful in the TiVo community for Carl to bring this to our attention, it's a huge step forwards in us understanding what might be making the TiVo sluggish at times. It could well be the load on Virgin's broadband network.