Ask anyone who has watched BBC for the last 10 years, and they'll tell you that BBC News has gone down the toilet of "entertainment as news/news as entertainment" and is pretty much exactly the British equivalent of CNN. The accents don't actually mean it's better.
Al Jazeera is a great choice mostly because it's not a Western viewpoint. Same with Russia Today who will happily poke at topics BBC and CNN dropped very quickly or never discussed at all, and it streams live online 24/7.
If it isn't blocked, there is also PressTV which is the Iranian CNN, certain to have a different point of view of the same global topics. All three broadcast in English.
I would love it if China had an English language news channel, just to hear their angle on the same major topics.