I am assuming you mean BBC iPlayer, because the news apps are fine on my HC Flyer. But be more specific because BBC has like 10 different apps. Some developers, such as HBO and BBC are way behind the times. Their apps are not compatible with Honeycomb. Look for tablet versions of the app, although I know there is no HBO GO tablet yet, which is pretty stupid on their part since the experience would be a lot better on a tablet than a phone.
Days of open internet are almost over as the biggies look for more revenue streaming from your wallet..Soon the internet will be a shell of its current self. With the government wanting their taxes and the big ISPs planning to charge extra for access to specific content (like facebook) and throttle your speed.