We are currently building bases in Iraq and doing so speedily.
They are NOT in the Anbar province, but close to the Iranian border.
That suggests the US military has already considered the scenario you suggested, and planned for it.
The Brits in Basra would not be so trapped as you might thing, considering you're on the coast. You have many options for either extraction or resupply. You can head south through Kuwait if need be, and there are options by sea, though those might possibly be interdicted by use of Iranian rockets on naval vessels.