The Police, along with NHS, Fire and other Government bodies use a Tetra (Airwave Network), its a built for purpose National Digital voice and data Network on the lower part of the UHF Spectrum.
The Personal Radios (lapel, broach type you see) are low power Tetra Handsets, the Mobiles are also Tetra Units designed for Mobile and Desk Top use. The selectable channels, aren't actual channels as such but are predefined Individual Identities or Group Memberships of users, in other words all Users are on the same Network but each radio unit is programmed for a predefined use on a who needs to listen, talk, use data etc basis. Each Units Identity and Electronic Serial Number is also linked and authorised to the Network every time its switched on, makes a call or moves into another Cell location. The digital Voice and Data traffic is also digitally encrypted so it can't be eavesdropped.
Tetra is late 90's technology, the UK was the first in the World to build and operate National Tetra Networks, Two Networks were allocated, one Open User Commercial (Dolphin Telecom) and the other a Closed User Government (BT Airwave). The Commercial one was built and owned by National Band 3, a successful UK wide National Trucked Radio Network, it was then bought by a Canadian Company who shut down the Trucked Radio, transferred the Customer Base to its new Tetra Network, wrongly tried to compete with the UK GSM Mobile Networks and basically messed it all up and it went bust, so the Commercial Dolphin Network was dismantled a couple of years after being built never to raise its head again.
The Government Airwave Network was built a few years after the Commercial one, originally by BT, then owned by a few others O2 etc, and now owned by a French Company. The Network is still in its original format, having been, expanded, tweaked and modified somewhat, current plans are and have been for some time to replace it with a more up to date, more spectrum efficient modern Digital Network, despite the fact it works and does was it says on the tin.