Police officers have the power to stop and search anyone under the Terrorism Act 2000 to discover whether he has in his possession anything which may constitute evidence that he is a terrorist.  They do not need a specific reason, your presence in a specific area is sufficient excuse.  Cameras may be seized and retained until it is determined whether photos have been made for terrorist purposes.

Refusal or non-cooperation will result in arrest and punishment by fine of up to £1000 and/or 6months imprisonment.

You are not obliged to give your name and address or explain what you are doing, but in practice you may be arrested on some other pretext if you do not.

The authority for these stop and searches arises under Section 44 of the Terrorism Act, which is why they've become colloquially known as S44 searches. They are highly contentious as they appear to be widely misused. You should ask police to explain whether they are looking for terrorists or trying to deter or delay you. Also make sure they issue you with a Search record. Consider making an official complaint if you feel the search was carried out wrongly or for the wrong reasons. Also fill out Liberty's search monitoring form 

A very commonplace experience is to have security guards run out of a building you are photographing and insist that you cannot because the management do not allow it, because the building is copyright, because it is private property, because you need permission, that they will have you arrested, or you will be sued. They have no authority nor legal basis for any of this so long as you are photographing from the public road or path. They have no power to demand you delete pictures, and no power to demand your name and address.

In most cases, if explanation doesn't do the trick, calling the police is a good idea.

Press have no special privileges of access in UK, their entitlement to photograph is identical to every other citizen. The National Press Card serves only as a means of identification as a member of the press.  Whether it is accepted as such by police is variable.

In some circumstances press cards do achieve greater access, but this is dependent on the operational priorities (or whim) of the police. Press may be admitted to an area that has been closed to the public because of an incident or for security reasons. At other times press will receive extra attention to prevent them photographing even when surrounded by a sea of amateurs clicking away with digicams and mobile phone cameras. 

Photographing children in public places is, for most children, exactly the same as photographing adults under the same circumstances. That is, there is no right to privacy and hence it is legal.

The exception is children (and vulnerable adults) who are wards of court or subject to a child protection order, or on the 'at risk' register. The Children Act 1988 creates special rights of privacy ('the rights of the child') which make it an offence to publish any photo that might place them at risk from, say, an estranged violent parent by divulging their location. A photograph of a child in a public place wearing school uniform, or accompanied by others whose whereabouts are known to the would-be assailant, might conceivably do this.

The Children Act is also the cause of problems at sports clubs and similar venues, as the supervising adult has a legal duty to safeguard these enhanced rights to privacy. And since part of that right is confidentiality about the child's status, usually they will not know themselves which children in their charge the Act applies to. Their safest course of action then becomes one of challenging any photographer as an imminent threat.

But by far the biggest issue surrounding photographs of minors is public fear of paedophiles. There seems to be a widespread assumption that the only possible explanation for any adult photographing children who are not their own is that they are a pervert with a camera. Proceed with extreme care and sensitivity, and if at all possible ask permission.

The Serious Organised Crime and Police Act 2005 creates 'designated areas' where  demonstrations or protests are suspended unless prior permission from the Secretary of State has been obtained.

This should have no bearing on photography but in practice it does not work out like that. Anyone photographing unauthorised protest within the designated area of 1km from Parliament, Westminster Bridge, New Scotland Yard is liable to be regarded as a protester rather than a photographer and detained or arrested, and that includes professionals reporting on events.