Why should the BBC pay?
Isn't it in the interest of the ISPs to reduce bandwidth? How about if the BBC just provided the software (already a substantial investment) to provide cached streaming of content and left it up to ISPs to implement it (within contractual agreements) and pay for it, since it will in effect save the ISPs significant bandwidth and therefore money to implement it. Combine that with some DNS based service discovery in the software to identify the closest servers (and a way to temporarily circumvent the broken server, in case the server has issues) and I think the BBC could save a whole lot of money.
I think that most ISPs (who do not have conflicting agreements regarding content) would gladly provide caches for P2P applications also, if it would save them money. The biggest issue is that most P2P protocols aren't easily cacheable, and P2P architects who don't cater for this should be beaten.