[jdietrich]

I can think of a few factors that might be relevant.

British police have been enthusiastic adopters of drones due to ongoing budget constraints. Drones are a lower-cost alternative to helicopters or large search teams.

British geography is well suited to small quadcopters. Helicopters or fixed-wing aircraft are much better suited to SAR operations in large unpopulated areas, but a quadcopter is often a better solution if you're searching a small area with dense terrain.

Britain has an exceptionally large number of CCTV cameras, which has created a base of knowledge and experience in using remotely-operated cameras as part of a search operation.

The Civil Aviation Authority has taken a relatively progressive approach to drone regulation. It's fairly easy to get licensed as a professional operator, and comparatively straightforward for those operators to get permission to fly in potentially high-risk scenarios (e.g. night flying over a densely populated area in controlled airspace).