This is a subject I've had to have some familiarity with since I started doing street photography back in 2007. One of the most important aspects of the law relates to the expectation of privacy. As an example, if someone sits by a cafe window during daylight hours they can't expect privacy. If they sit at the back, as far away from the window as possible, they might expect privacy if they can't be seen from the street. At night, when you can see all the way to the back, can they then expect privacy? Well, that might have to come down to what a court decrees. So the best advice IMO is to be careful.
It's also advisable to be aware of what constitutes 'publishing' of a photo. Uploading it to a public forum like this one is publishing, as it uploading to Flickr, Smugmug, Instagram, Facebook, or anywhere else the public has access to. I'm only mentioning this because before the rise of social media some people thought that publishing meant having it printed in a magazine, newspaper, or book.
There are also some places where photography isn't allowed (think military, police, air force, etc), and some where it's at the discretion of the owners (think shopping precincts). And some where professional photography isn't allowed but amateur photography is, provided that you don't use a tripod or monopod as, for some reason, the security people think they're to be considered as pro gear.
Anyway, I've uploaded a few things to my Dropbox. Feel free to download them. The first is the most useful: a guide to photographers' rights in the UK. This dates back to 2009 but as far as I'm aware nothing in there is incorrect. The second is an explanation of the Section 44 Terrorism and Photography Act of 2000 by the Chief Constable which dates from around 2010. The third is a copy of a letter from Ivan Lewis MP re photography in public places. I hope this helps.
UK Photographers' Rights
Section 44 Terrorism and Photography
Shared with Dropbox
www.dropbox.com
Home Office photography letter