As far as I can tell, it's largely a data or modeling problem.

Weather radars exist in most of Europe, including all of Western Europe. What's missing is somebody actually getting that data (which is not open in all countries) and feeding it into a short-term precipitation prediction model like Dark Sky (now Apple) does in a few regions.

Currently, in regions where it's not available, I just do that manually: Look the rain radar data for the last hour or so and extrapolate linearly based on wind direction. You'll miss rain that's just starting or stopping or sudden changes in wind direction, but it's much better than what many apps offer.