It is not illegal to take photographs or video footage in public places unless it is for criminal or terrorist purposes.
There will be places where you have access as a member of the public, but will have to ask permission or may be prevented altogether. These could include stately homes, museums, churches, shopping malls, railway stations and council / government buildings. You need to check the situation out on a case by case basis.
The taking of photographs of an individual without their consent is a civil matter. Taking a photo of a person where they can expect privacy (inside their home or garden) is likely to be a breach of privacy laws. The other issue to consider is what you plan to do with the photograph afterwards. 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, many media organisations are international and will not accept an identifiable photograph of a person without a signed release. If the photo could be seen as defamatory in some way then you would leave yourself open to civil proceedings.
The country is in a heightened state of alert (and will be for many years) because of potential terrorist attacks. So called 'soft targets' are particularly vulnerable. Security staff, the general public and police are much more aware of anyone taking photographs and you may be approached by someone, such as the police, when you are taking photographs near or in potential targets. Generally the police cannot seize the camera or memory card unless you are committing an offence or suspected of terrorist activity.
Finally, it is a specific offence to elicit information (which would include photographs) about members of armed forces, police officers or the intelligence services, which is likely to be useful to a person committing or preparing an act of terrorism, or publishes or communicates information of that kind. The law does not state that the person who gets the information has to use the information for terrorism purposes, just that the information is likely to be useful to a terrorist. There is a defence of 'reasonable excuse' for this offence, but it would be for the suspect / defendant to raise this matter.
Photographers need to be aware of this provision and be cautious when taking such photographs. The sort of occasion when it could cause a problem may be, for example, at an anti-war protest, when there may be a number of counter terrorism and intelligence operatives working in the area. If an officer makes an arrest for this offence it could cause a lot of unnecessary time wasted for both the officer and yourself, although that may only be until the facts are clarified.