I've stopped watching / reading BBC news altogether as I no longer find it trustworthy or unbiased.
I have the Guardian app on my iPhone, which I like a lot — latest news updates in a feed, lots and lots of news stories, and longer reads available — and the Times app on my iPad. The Times is odd because it's not continually updated during the day. The app is basically like a physical newspaper: it's the news at the time it was printed. But it's well done.
On TV I now watch Sky News.