Sectarian violence has been worsened by outside influences and actors. It is widely thought that the Arab states, like Saudi Arabia, are supporting Sunni groups, and according to official U.S. sources Iran is supporting and arming Shia militias.
The Shia militias are predominant in the British controlled south, where Iran has direct border access, meaning if they are arming and funding militias, it is easier than it is for the Arab states to support the Sunni groups. To make matters worse, Iran has the added motive of the ever-present danger of a U.S. attack, making Iran determined to make the U.S.'s life difficult in Iraq. Unfortunately Britain suffers first and worst from any of Iran's pre-emptive defense measures.
So, having said all that, the fact that British troops have been able to hand-over power to the Iraqi forces in all but one of the southern provinces they controlled without any severe consequences says a lot about the abilities and strengths of the British army.
It also says that the MoD has realized the point I have made in this article: British troops can only maintain a certain level of security; the attacks leveled at them prevent them from bringing total security and peace. Therefore, when they have trained the Iraqi police and army in that province sufficiently, it is right for them to hand over control. After all, we will never know if they can do it unless we let them try.
I'll finish by saying that I don't know enough about the situation in the south — figures, polls, etc — to really say whether it is a defeat or not. But pulling out to a safe distance, removing a target that creates its share of violence, avoiding the loss of anymore British troops while continuing to train Iraqi forces, monitor the situation and be on-call if needed, sounds like the best solution all round. As the saying goes: you'll never know unless you go.