Just off the top of my head, both Demon and Clara don't specifically say you can't serve from your adsl or dialup connection - I'm just checking their aup's again now.....
Demon for instance provide you with a static ip address by default, and Clara will sell you a static ip for something like a one off fee of £25.
However, on the downside to serving on adsl, you are pretty well restricted to 256kb upstream, unless you're on an SDSL exchange, where it'd be somewhat quicker
My Rib's website for instance is hosted on a box at work, and that's through the ADSL which is fine for my needs, but I suppose if more than say 6 or 7 people were hitting it at any one time, then it would become painfully slow.
One possibility I'm looking at for my site at the mo is www.rackshack.net
which is based in the US, but gives shed loads of bandwidth for the money, which would be very handy for streaming videos