Another point to be made is that the Brits have gone into total force protection mode down there. The Islamist mafia, Iranian intelligence, and oil smugglers (who are oft-times all the same people) have veto power over all that goes on in the south. Trust me on this one.
al-Sadr's top aid laid out the Madhi Army's plans for talking over Iraq two months ago to the Washington Post, he plainly said they plan on starting a civil war and winning it and then consolidating their victory meaning killing their Shia rivals.
The Madhi Army plan is simple first get an all out civil war going, that will allow the Madhi Army to expand massively from 30-40k to 300-400k thanks to the four million poor citizens of Sadr City which would provide a great pool for Madhi Army fighters. With help from Iran they could equip these fighters.
In a year or two the Sunnis would be driven out of Baghdad and nearby cities and deep into the far west of Anbar. At which point the Madhi Army would use its several hundred thousand strong militia to overpower the rival Shia militia the Badr, thus allowing them to control Iraq. After that I expect with Iranian and perhaps Turkish help they will start a long with the Kurds.
This is why the US can't just sit back and let a civil war occur.