Is this actually based on GPS (or similar) on the trains, or is it just interpolating signal times (which are waaaay coarser)?

Not affiliated with the site, but it's almost certainly just the Train Describer feed from Network Rail to observe headcodes stepping through berths, and then doing some proprietary interpolation within berths to guess where the trains are, probably using fairly coarse inputs like train class, rolling stock type and line speed. It's possible it's not even doing that, and they have just built a model that observes typical passage times between berths and they average that out.

TRUST (reporting system that describes train movements as they've happened) does accept updates by means other than the Train Describer, which might include GPS if the unit is equipped, and in many areas is dependent on signallers making manual reports (which may not be made immediately). They might also use TRUST as a data source, especially in non-Track Circuit Block areas. The rate of GPS updates is not going to be anywhere near as frequent as those train position indicators that appear to move here in "real time" across the map, so however they combine data sources, their site is trying to be clever in guessing train location.

It goes without saying: this sort of map is highly likely to be wildly inaccurate and isn't useful for anything safety-critical.