The UK has some privacy relevant laws, but the laws for photography are generally permissive, which means that as long as you're in public, you can probably take the picture.
Can I Shoot Footage in Public without Consent?
Yes, you can almost without restrictions shoot anything as long as what you're seeing is visible from public property. You are allowed to shoot people, including police officers or other government officials.
It is not illegal to take photographs or video footage in public places unless it is for criminal or terrorist purposes.
Some exceptions will apply depending on which situation your subject is in. A court case for example showed a man in front of a drug rehab clinic, who sued against being depicted in this private moment.
Children are an exception to this rule, they have a stricter right to privacy.
Can I publish Photos taken of Strangers without Consent?
Yes, unless you show them in a vulnerable or very private situation, such as grieving, intoxicated, etc.
However, the police recommends:
If the picture is of an individual, perhaps as a portrait or character study, and you intend to publish it in any way (on the internet, in a book or at a gallery), it would be appropriate and may avoid unnecessary complications if you ask that person for permission
Can I use Street Photos commercially?
Yes, you can also use the photos commercially.
Can a Security Guard demand to see my camera or force me to delete my photo?
No, unless you're suspecting of preparing an act of terrorism. It is unclear what the legal threshold is for being under suspicion for that.
Note There are a few cases of celebrities against the yellow press we could find so far, but no cases of street photographers vs somebody else. Please add them, if you find them or let us know about them.