Weekly Weather Report for Taunton, Somerset, United Kingdom. Looking at the weather in Taunton, Somerset, United Kingdom over the next 7 days, the maximum temperature will be 15℃ (or 59℉) on Sunday 16th April at around 3 pm. In the same week the minimum temperature will be -1℃ (or 30℉) on Thursday 20th April at around 3 am.