The problem in Basra City is that we don't know exactly what is going on in there. Its a black hole (to give the Brits their due, they may not be in the city, but they are not sitting out at the airport--they are doing ops along the border and in other areas).
Also, the Mahdi Army (JAM) is not a monolith. In fact JAM in Basra is probably only tenuously linked to the larger JAM (Sadr's powerbase is more up in Sadr City). I would not assume that events in Basra are linked to the current up-tick in Sadr City in any real planned manner. I have not heard or read anything about the Sadr ceasefire writ large. This could be an actual extention of the "cleansing" that Sadr wanted to effect through the ceasefire in order to bring his movement more under control. The snippets of news reporting are always misleading.
Basra is a place that the Government must control if it is to control Iraq. This fight probably had to come at some time. The government may assess that they want to have it while the Coalition Forces are still here in some strenght and holding the Sunni threat at bay (which the Government interprets as the Concerned Local Citizens or Sons of Iraq). For the past few months, the Iraqi leadership has been trying clean up the Army units (moving non-locals in) and the Police in Basra. Arguably, they have probably been more successful in the former than the latter. It would also be interesting to see where the Governor of the Province is in all of this (Fadhila Party-neither Sadrist nor associated with the ruling coalition). If you remember news reports from last year, Maliki tried to get him removed, but failed. There was tentative coming to terms between the two. Also not reported is whether the oil flow has been greatly affected. I'm guessing not. The pipelines don't run through the city and the unsaid "Prime Directive" of competing groups in Basra Province has been to not stop the oil flow--too many people from all sides are making money on it.