They're constantly mucking about with the Anytime connections and I have got considerable mileage from the Emergency Anytime number - 0800 5879089 - that a PPRuNer published here a little while ago. I recommend it to anyone who has trouble with the 0808 number.
I have most trouble connecting in the first place but if I get a solid connect it usually stays that way until I log off.
There was a news item recently about a gang of villians who had stolen the entire set of BT reserve Servers to export the hardware - particularly motherboards and processors - to embargoed countries such as Iraq. Other major companies had also suffered similar losses.
I bet part of the BT Internet problems stemmed from that loss alothough they have never owned up to it.