Every issue of the Radio Times from 1923 up until the end of 2009 is on the BBC website. (The BBC sold the Radio Times to Immediate Media not long after that). So that can help track down a lot of radio and TV programmes details:
https://genome.ch.bbc.co.uk/issues
However it won't help with later dates. It also won't help find ITV programmes in the years when the BBC and ITV each jealously guarded their copyright protection, so that viewers who wanted to find out what was on each of the two channels had to buy both the Radio Times And TV Times (as neither publication was allowed to list programmes from the rival provider).
Your best bet for finding other programming is to consult the Television & Radio Database
https://tvrdb.com/ but that only goes up until the end of 1999.
Other than that, you might need to try Google searching, possibly improving your search criteria by using the 'custom date range' function.