The police helicopter usually operates under flight category B, which has priority over everything apart from emergency traffic. However the pilots are very pragmatic and know when a particular detail is likely to cause disruption to scheduled aircraft. In this case they will do everything possible to minimise their impact on normal operations, such as flying at very low level or moving their operating area slightly. However the bottom line is that if a police helicopter really needs to be in a difficult place operationally, then so be it. Scheduled traffic is then delayed to accommodate its operation.
The police helicopter requires an ATC clearance to enter the London and London City Control Zones just like any other aircraft and the pilot must maintain a listening watch at all times. ATC transmissions take precedence over police transmissions. The police helicopter pilots are extremely professional and competent and know the airspace intimately. They are given "free range" to carry out their duties as much as possible, but there is often much liaison occurring between the various ATC agencies within the Control Zones.