Read what Michael Rubin of the CPA and AEI after returning from his post. He claimed that the Brits support any form of dictatorship in Iraq and have extremely close relations with the Iranian government.
Helping setting up a Shiite theocracy in Iraq would certainly help them score political points in Tehran. Plus, what would become of a Shiite Iraq sitting next to a Shiite Iran, especially given the fact there's no Iraqi army anymore ?