Apart from looking at unit diaries, if they exist, you could look at these reports from the UK National Meteorological Archive: https://www.metoffice.gov.uk/binaries/content/assets/mohippo/pdf/b/i/may1940.pdf https://www.metoffice.gov.uk/binaries/content/assets/mohippo/pdf/i/h/jun1940.pdf There is also an article which may help, no link to it, but a reference you could search for: Met Office - Detailed Record View Mark
At the bottom of this page is a link to the Daily Weather Reports, a series of documents of which I was not previously aware was available. Thank you, Orwell1948 for the link to the page. Mark
The Met office digital archive also has daily weather records for Great Britain which extend over northern France
