Folks, the Met Office, based in Exeter is the UK's leading weather data & forecasting service. It is a gov.uk department and is not privatised! The BBC ceased it's contract with the Met Office some 5 or so years ago. The BBC now takes its forecasting service from Meteogroup.
I think, but I'm not sure, that Meteogroup take raw data from the Met Office (& maybe other sources) and from that create forecasts which the presenters tweak for broadcast. The Met Office however is still the source of Weather Warnings which always take precedence over any day to day forecast. Be sure to read them when you see one!
If you can accept that the UK is one of the most challenging countries to forecast for; Atlantic to our west & European landmass to our east, you might imagine the challenges any forecaster has to overcome. Also take into account that presenters will usually focus on the most prevalent weather to be expected. Weather can be very localised too so one man's accurate forecast might be not so a short distance away.
Years ago I believe farmers had an instinctive sense of what the weather might hold. They were tuned into the natural world, knew their territory and relied on experience alongside any forecast which in the old days probably came over the radio waves! Women & housewives too, likely could "smell" rain or snow in the air, checked out the sky, and thus hesitated to peg out washing or not? Has time has dulled our instincts? Who knows.
You can find out more at www.metoffice.gov.uk