There are different types of error from weather forecasts. Sometimes the forecast is correct, but the timing is wrong. Sometimes there might be rain which is too light to be picked up by rain radar, so it won't be picked up. I'm in East Anglia, and so there aren't any hills to mess up the predictions.
The BBC use forecasts from MeteoGroup
https://www.dtn.com/about-us/company-profile/ instead of the Met Office.
For short term term "is it going to rain in the next 2 hours", I like the MinuteCast at Accuweather:
https://www.accuweather.com/en/gb/london/ec4a-2/minute-weather-forecast/328328 Its not perfect, but it does a pretty good job.
For "is it snowing?", then
https://uksnowmap.com/ is good. It plots the locations of tweets, where people give the first half of their post code, and a rank from 0 to 10 of the snow intensity (0 is nothing, 10 is a blizzard).
To get a feel for rain in the next half day, I like
http://www.raintoday.co.uk/ which uses the MeteoGroup rain radar as it also shows the intensity of the rain clouds.
For a forecast over a few days, then I prefer the Met Office
https://www.metoffice.gov.uk/ That has video reports which sometimes gives a better overview if there are uncertainties, and the text from weather warnings. The weather warnings are usually over-cautious, but its good to keep an eye out for possible problems.
For long term forecasts, then
https://www.wxcharts.com/ shows the predictions for the next couple of weeks. These predictions are from
https://www.ecmwf.int/ and are usually wrong in the detail, but often give a reasonable idea of the character of the weather.
