What was the weather like for an event in your UK family history?

The UK Meteorological Office Daily Weather Report provides a summary of the observed weather for each day for a selection of UK stations with charts and tables and textual descriptions of the weather on the day.
The format and content of the daily weather summary varies over the many years of publication.
You may find tabulations of observations every six hours, ot the same information in map format.
Expect to find a UK weather map. Some years will provide a broader scale northern hemisphere map, some images from weather satellites.

Produced since since September 1860, so back several generations, the Daily Weather Report is available free from https://digital.nmla.metoffice.gov.uk/archive/sdb%3Acollection%7C86058de1-8d55-4bc5-8305-5698d0bd7e13/. You have to narrow the selection down to the month, then scroll through that file to the date of interest.
A separate page at https://www.metoffice.gov.uk/learning/library/publications/daily-weather-summary provides access to the recent issues.