Airspace can be restricted by the setting up of either a Temporary Danger Area (TDA) or a Temporary Restriction of Flying Regulations (TRFR). Any one of the list of government Emergency Coordination Agencies (ECA) can set these up and this includes a Chief Constable. A TDA is mandatory for military aircraft but only advisory for civil aircraft, unless that civil aircraft is specifically instructed to vacate by the person with responsibility for safety of flight within the TDA (usually the ECA's representative ie Police/SAR/Ambulance helicopter and not ATC).
If a TDA fails to achieve it's objective, or in the case of some pre-planned events (political conferences etc) a TRFR may be established, which is mandatory to all aircraft. These are very rarely used as they take time to implement and require the Secretary of State for Transport's minions within the CAA to approve them.
Nobody likes to restrict airspace and it is usually only done for reasons of safety to protect any aircraft operating within the restricted area that may be limited in manouverability or lookout.
Press/filming helicopters can and do enter TDAs but it is a question of management. Just ask the police/SAR/ambulance helicopter for their consent (you may have to tell them that, as the ECA's representative they are empowered to give it!!!). Inform ATC that you have this consent and you are then good to go.