It's getting worse, but still not as bad as it could be. Basically, you're allowed to take photos of pretty much anything. It's not
what you're taking photos of, but
where you're standing when you take the shot. If you stand on any public area or any private property on which the owner has given you authorisation to shoot, you're good. The only exceptions to this rule could be seisitive areas/military installations, but you shouldn't really have a problem. It's true that that legislation has recently come into being that states that you can't take photographs of police officers. I don't suspect you'll need to, so just try to avoid that.
One important thing to note is that under the anti-terror laws, the police have the right to carry out a random stop and search of you, taking down your details such as name and address etc. If this happens, don't worry about it, they just get put on some record (supposedly) for a certain amount of time, or until the government has their next IT screw up

This is likeley to happen if you're taking photos 'seriously' i.e. spending a lot of time on composition, using a tripod etc, and has happened to me on a number of occasions. One time my friend was using my camera near the US ambassadors' house in Regents Park, just before the then President of the US George Bush was due to fly in and stay there for the duration of his trip in London. Another time, me and a friend were taking photographs in Parliament Square, spending a lot of time and using tripods, and the police pulled up in a van and did the whole anti-terror thing. It's nothing to be worried about really, you still have the right to shoot there, but equally they have the right to take your details down. If any other officers stop you for the same reason that same day, you can just show them the copy of your details you're given to show that you've undergone the process already.
Here is a downloadable PDF of UK Photographer's Rights:
UK Photographers Rights
Don't be put off by it. Have fun in London, it's a very exciting city. :thumbup: