Most of the time the police are fine in London and elsewhere in the UK - it's just a few incidents get highlighted in the media where the police (and security guards) have overstepped the mark and try to stop people from taking photos. From what I have read this generally seems to happen because the authority in question is ignorant of the law and what they can and can't ask ordinary people to do.
Common sense will usually see you through - for example if you're taking photographs in a protest march you have to expect that it might attract the attention of the authorities - whether that's right or wrong is a separate issue. These are the times we live in, I guess. But if you consider how many people visit the major tourist sights, such as Buckingham Palace or the Houses of Parliament, it's probably futile for the police present to try and stop that amount of people from taking photographs even if they could, so often in those areas you find yourself simply blending into the crowd.
I carry around a list of photographer's rights in my camera bag in case I ever get stopped when I am on a public street; as far as I am aware the law is different if you are on private property in the UK. Even if you do not wish to argue with a policeman it may make you feel more confident to carry a printout of your rights with you. It may sound obvious but just make sure any list of rights you are carrying is relevant (ie the law applies to the UK, not another country, and is current). The following sites might be of help:
http://www.sirimo.co.uk/ukpr.phphttp://www.photographersrights.org.uk/index.html Chances are you're unlikely to get stopped for taking a photo if you're aware of what's going on around you and you use your common sense, but that's not to say it won't happen!
On the underground tube system you're not allowed to use flash photography and there are regular reminders on the tannoy.
In relation to the last question by Windhorse I don't think it will stop people visiting the UK, but the fact this is even being discussed is definitely a bad reflection on freedom. Our government seems to have lost sight of the fact that cameras and photographs don't blow buildings up. I've been moved on by security guards in the past (never police) and have accepted what they have told me to do, but now I am more aware of my rights, depending on the situation, I might argue my point in the future a little more forcefully.
Enjoy your trip, and don't worry too much.