How can I find out what national and local events happened on someone’s birthday?

National and local newspapers for the day in question (and the days following) should provide news reports on contemporary events. Some national newspapers can supply back issues, or facsimiles of front pages on a commercial basis. Many newspapers are now available through the British Newspaper Archive website (available free of charge in the National Library of Scotland or with a subscription elsewhere) https://www.britishnewspaperarchive.co.uk/