There are several sources for historical weather information for the UK.
One of the most accessible as it hits the highlights of more extreme events is WEATHER IN HISTORY 11,000BC TO PRESENT. In half-decade periods since 1600, and even back further learn about the weather events that may have disrupted your ancestor’s life.
The British Meteorological Office Digital Library and Archive website includes various resources listed under UK Observations. The most valuable if you’re looking for daily information is Daily Weather Report /Daily Weather Summary with data from 1860 onward. Choose a date in your UK family history and find out the weather on that day.
British newspapers often covered weather including in regular commentary columns. If you have access to newspapers.com try The Guardian, available with the Publishers Extra subscription. Try newspapers available through Findmypast and the British Newspaper Archive.
A recent source for monthly rainfall, freely available files ready to be loaded into a spreadsheet, is the product of a crowdsource project described in the article Citizen Scientists Digitized Centuries of Handwritten Rain Data.