The UK law does not prevent you from taking photos or video in a public place excluding professional photography in Trafalgar Square (Bylaws 2012), parliament square and Royal Parks.
You should not be taking photos or videos of an obscene nature or of private places from a public space like using a zoom lens to take photo of someone’s bathroom as an example.
There is no assumption of privacy in a public place and no one can ask to view, ask for a copy or delete your image or video, this also includes the security or the police.
The police can ask to view of the image or video if you are been detained for the purpose of search, or a copy if you been detained and materials has been seized.
Shops and shopping centres and certain places that are public places that are privately owed will have there own rules on taking pictures or videos and as such will not allowed to take photos or videos without the permission of the owner.
They may turn a blind eye to certain situations, for example if you were taking a selfie or a photo of your friends and family enjoying your shopping experience, but if you are asked to leave, you will have to stop and leave as at this point your will be considered a trespasser.
Taking photos or videos can be class as harassment, but it’s not as simple as just taking a photo or video of someone.
It can only amount to harassment if you take pictures or videos on at least 2 occasions when the person knew or should have known it would amount to harassment. (s1. Protection from Harassment Act 1997)
This does not apply to street photographers if:
Subsection (1) does not apply to a course of conduct if the person who pursued it shows-
(a) That it was pursued for the purpose of preventing or detecting crime.
(b) That it was pursued under any enactment or rule of law or to comply with any condition or requirement imposed by any person under any enactment, or
(c) That in the particular circumstances the pursuit of the course of conduct was reasonable.
You can be searched under the Terrorist Act if you take photos or video of police, Military and places, buildings of national security.
Which can amount to offence if publishing or communicating information about members of armed forces etc..
It can be unlawful for the police to use the terrorist act when you’re taking photos or video of police in there policing duties without strong evidence to provide assistance to terrorist.
GDPR data protection regulation means you can’t post images or videos on social media.
Except for personal or household use, but there are special purposes that allows an exception under article 85-2 under the freedom of expression and information for journalism, academic, artistic and literacy propose.
Photography advice | Metropolitan Police
Microsoft Word – Trafalgar Square Byelaws 25Jan2012.docx (london.gov.uk)
Protection from Harassment Act 1997 (legislation.gov.uk)
Photographers Rights & The Law in the UK – Guy Butler Photography – Commercial
Copyright and GDPR for photographers – Intellectual Property Office blog