The BBC are giving prominence to an Israeli invasion of Lebanese territory because - guess what - a lot of innocent people are being killed by it. Given that we value lives equally (We do, don't we?), shouldn't coverage be proportionally aligned along with the number of civillian deaths?
Of course, if you look at the BBC
lead item, it states the number of deaths, and what's most important in the political context, etc. Because the key news here, is not that there are rockets landing on Israel,but that there is an immenent humanitarian disaster, and the possibility of a region-wide conflict.
I'd note, again, that the BBC has given prominent TV coverage to rocket attacks on Israel; but in the present context it is far, far more important in an international context to report what is happening in Lebanon; especially because it's only strengthening support for Hezbollah (and a key part of the political context is the influence Hezbollah has over the people of Lebanon,especially if you actually want to a) have a democratic Lebanon and b) have that Lebanon capable of 'managing' Hezbollah).
EDIT; a side note; the majority of the worlds' opinion being against Israel doesn't constitute support for Hezbollah. It constitutes condemnation for an attack on the civillian population of Lebanon, including the democratic government, in response to the act of a 3rd party terrorist group. We expect Israel, as a free, democratic, stable country, to act to a high moral standard. Many people, I think, view Israels actions as immoral, excessive, self defeating and dangerous for global stability.