The Met Office has a freely accessible Digital Library and Archive.
It is possible to view or download a pdf file for the Month in which you were born.
(or any period you may wish to investigate)
It will include full records for each individual day in that month.
These can be large files. Mine is 66.9MB
There is information from 1860 onwards.
Don't expect the sort of simplified charts seen on TV forecasts.
These are full reports / logs of temperatures, sunshine, rainfall, wind, charts, etc..
Presentation of the information varies depending on the methods used at the time.
This is a chart for the day I was born;

As I was a bonny, bouncing war time baby I was not surprised to notice some of the pages on my charts were marked SECRET at the time. No sense in letting the enemy know when the weather would be ideal for a bombing raid! All are available to be seen now.
The Met Office Digital Library and Archive can be found HERE.
You can start refining your search HERE.
Information accessed contains public sector information licensed under the Open Government Licence v3.0.