In general photography does not require permission in public places. However what sounds like a pleasantly simple rule is complicated considerably by questions of what exactly comprises a public space. There are a number of important restrictions that apply:

• Photography in public places such as roads and public Rights of Way can be problematic if you use a tripod or other equipment that causes obstruction or hazard to the public. Unfortunately the offence of obstruction can be committed merely by standing still, and the threat of arrest for obstruction is often applied by the police in order to curtail photography.
• Obstruction of a policeman in performance of his duty can be invoked if you fail to follow police instructions or co-operate.
• The Terrorism Act 2000 (section 44) allows police to perform a stop and search without giving any reason whatsoever. This is the main legislation being deployed against photographers at present.
• The Official Secrets Act 1911 prohibits photography that threatens the security of the state:
  • Military establishments and munitions stores, aircraft and ships
  • Civil Aviation property and naval dockyards
  • Railways, road, waterway, power stations, waterworks, nuclear power stations defined as prohibited places by the Secretary of State.
  • Telephone exchanges and communications centres operated by the Crown
  • Anywhere else that is a prohibited place by order of the Secretary of State
• A great deal of the UK is under private ownership and although open to the public does not constitute public spaces. Examples would be shopping malls, carparks, markets, office developments etc. EG Spitalfields Market & Canary Wharf are guarded by private security who appear unable to tell the difference between a camera and a rocket launcher. 
• Some public spaces have laws which explicitly restrict or prohibit photography, eg parks, Trafalgar Square, Parliament Square, Typically amateur photography is allowed without a tripod, but photography for commercial purposes is forbidden without a permit.
• Certain public spaces are subject to SOCPA restrictions. The designated areas currently are 1km around the House of Commons, Westminster Bridge, New Scotland Yard, St Thomas' Hospital and the Channel 4 site. Although SOCPA restricts public demonstrations rather than photography, photography is treated with heightened suspicion at these locations, and photographers covering either authorised or unauthorised demonstrations have frequently been treated as demonstrators and threatened with prosecution even when carrying bona-fide press credentials.