I’d be very surprised if the Brits pull out completely while the US is still in Iraq. We’ll still maintain a presence there.
I hope that the surge does work and Petraeus does seem the right guy for the job. One key problem for the British, as I understand it, has been the number of troops available for Iraq. With UK forces on the front line in Afghanistan also we’ve had very limited resources to take on the militias in Iraq (not least in troop numbers). Of all the countries deploying troops to Iraq, only the US and British appear to have been ready to fight. With all due respect to the other nations involved (and their brave troops), their deployments appear to have just been political gestures. As with Afghanistan, it would be great if our other allies would pull their weight too.