We surge south. The current British presence is around 5500 troops. Quadruple that with Iraqi augmentation and confront the Iranians directly. Break the local militias if they resist. This is absolutely attainable.
This article mirrors the infamous one in the NY Times of a few weeks ago in that it gives the impression that the military situation is so dire that we or the Brits would be lucky to be able to safely retreat. That may be what a lot of people on the Left are desperately hoping but it simply isn't the case.
It will have to end up being some kind of "internal" Iraqi surge. Probably have to find somebody up north in the capital to come down on the scrubs in the south. Kind of like "triangulation" where they play the wogs against each other.