Thanks Saab, that's the sort of technical stuff I was curious about! I guess I'll never find out for sure (as BT seems to have fixed it now), but that level three layer, IP addressing bit seems to make sense and fits in with my symptoms.
I went on a short course last year covering IP addressing (etc), and it all made perfect sense while the bloke was teaching it. Bewildered when I thought about it ten minutes afterwards though.