The BBC has a mobile page. Using the preferences link at page bottom you can experiment with various versions and bookmark the one you like. I have a version on my iPhone "home page" as an icon -- next to Google News mobile, the disappointing NYT reader, and the excellent Google Reader Mobile.
The BBC has also announced streaming audio support for the iPhone over WiFi only using their evil iPlayer service. This service allows only 7 days of access, in contrast to a far superior podcast alternatives that allows unlimited access after download. Evil, definitely.
Earlier versions of iPlayer were Flash based and wouldn't work on an iPhone, so they've had to concede to Apple's non-Flash policy.
The BBC announced this, but they don't say how to access iPlayer. If you go to http://www.bbc.co.uk/iplayer via a 3G connection from the US you get the Flash version -- it won't work. Comments point out that iPlayer service is UK only, so US users would need some kind of proxy service to test.