I'm happy to say that in the U.S., uniformed authorities are just now, finally, beginning to wake up to the realization that citizens/civilians have a right to record them doing their duties. As a prior poster noted, there have been some court cases that went against the uniforms, and the right to record has been affirmed by at least one higher state court. Some police departments have issued guidance reminding their officers that citizens have a right to record them.
I'm the type who will tend to side with police if there is a grey area of right and wrong, but it's clear to me that there is no legal or moral justification for prohibiting the recording of a uniformed authority performing their duties in a public place. It's no different, in my opinion, than the public nature of court or legislative procedures.
The argument about preserving some sort of security advantage, through secrecy, does not hold water, in my opinion. That argument is in the same category as the idea that police can tell someone not to photograph a bridge because a terrorist might want to have photographs of a bridge. The bubble of secrecy is already shattered when a civilian is standing there watching, and very little further is lost if that civilian happens to hit 'record' on an electronic device. That said, I DO support a prohibition on recording, for security purposes, in areas where authorities control access already. Say, for example, a security checkpoint where one must show ID and pass through a metal detector. If they want to have a sign that says you can't take cameras in there, that's fine with me.
I think a good rule of thumb is to ask before recording someone, unless that person is performing an official government duty, in which case, in the U.S. at least, it's the right of a citizen or other civilian to record so long as he or she is not interfering with the official. In that case, it's still important to be polite, maybe saying something like, "I'd like to record you, but I'll be sure to stay out of your way." Asking permission might seem like a polite way to broach the subject, but if the answer is no then you are already at odds with the official. Best not to ask. In my opinion.