The Met Office is the UK's leading meteorological service. The BBC uses data that the Met Office provides in raw format to the BBC's current affiliated forecasting service which for now, is no longer the Met Office. The Met Office collect data and sells it to all sorts of weather dependent outlets: airlines, oil rigs, banks, supermarkets, wind farms, utility companies, farmers, balloonists, to name just a few.
Weather forecasting is not an exact science and if an area is large eg The South West, the forecast will show what is expected to be the most significant weather across that region. "Weather" can be very localised. Sunny where you are but, raining & thunder five miles away. Who is to say that forecast is right or wrong? No doubt many of us have experienced localised weather when travelling for example, a motorway. In & out of rain or showers albeit a forecast also gave both, eg "sunny periods & showers for some".
Many forecasts with symbols are computer generated so go by those symbols but backed up on the Met Office website & app by a regional forecast written in words by a hard working forecaster. There's lots goes on behind the scenes at the Met office so believe me, it's not just a meteorologist on the telly but entire industries who use their services & are glad of it.