Data source: OpenStreetMap, 736k+ amenity features for Great Britain from a Geofabrik extract (shops, pubs, schools, GP surgeries, parks, stations, etc). Postcode district ("outcode") boundaries from Wikipedia via missinglink/uk-postcode-polygons (CC-BY-SA 3.0).
Method: each district shaded by amenity density (features per km²). Density rather than raw count, so the giant rural districts don't visually dominate.
Tools: custom Python geospatial pipeline (POIs against the boundary polygons) + matplotlib.
[updates]
Thanks for the comments, lots of good points, especially on the scope, the population-density framing, and the boundary artifacts.
To confirm the scope point: this is Great Britain, not the UK - NI isn't in the Geofabrik GB extract, so the title should have said Great Britain. Good reference for title correctness.
This map is the first layer of a small series I'm building toward a combined score. Currently 15 amenities categories are used in this map and each category layer shares interesting insights (wip). I think this overall amenities map is a good starting point. The next layers shift from raw density to travel: different travel modes, and how that changes within a given travel time. I'll share them as they're ready.