Bear in mind also, that although you can record the police, any such recordings are considered to be evidence. You can therefore take no 'pecuniary' interest in them. What that means is that you cannot use them for anything other than legal evidence in court. If you distribute the recordings, or use them in any other way, then you can be asked either not to, or for remuneration, by those persons in the image. This is, however, a bit of a grey area, which is exactly why the press get away with it, because its usually too much hassle and expense for a private person (even a very rich one!) to take the press to court over it. Besides, if you distribute the images, ie youtube them or whatever, and then wish to use them as evidence against the police, you may find the court unwilling to accept them.
I myself have had press images showing me whilst at work pulled for 'legal' reasons!