I suspect that Charlie and Camilla will be sent over to run the affairs of state. (and also to keep them out of Mummy's hair)
The quality of tea will improve greatly as you tossed the last decent shipment into Boston Harbo(U)r. The Washinton monument will be replaced with one for King George da Turd. The Lincoln monument will be renamed in hono(U)r of Benedict Arnold. The White House will be renamed Suckinham Palace and fish & chips will be sold to tourists in the Rose Garden. Schoolchildren will no longer waste time reciting a Pledge of Allegiance, as the time will be better spent learning to bow and courtesy.
You will be eligible to send athletes to represent you at the Commonwealth Games. Your status as a colony could be reviewed within a decade possibly making you eligible for annexation by Canada. Of course this would be subject to the approval of Stephen Harper.