The data behind these comes from the Darwin feed (National Rail's real-time data) which is surprisingly good once you get past the initial authentication setup. Network Rail also publishes movement data via their OpenData platform if you want to go deeper - actual track circuits and signalling block occupancy.

What I find interesting is how these physical displays handle the inevitable "ghost trains" in the feed - cancelled services that still show as running, or trains that briefly appear in the wrong location. The software problem is messier than the hardware.