Well, I would have a problem with British police on the streets of the US.
Actually that has happened. There are exchange programs. A few years back there was a human intrest story in the Cincinnati Enquirer about an English policeman who spent a month (I think) patroling the streets in Cincinnati. He was partnered with a Cincinati policeman. He did not carry a firearm, which he never did anyway, but otherwise was in his normal uniform.