On March 22, 2021, the BBC will stop a number of servers that until now provided live MP3 streams of BBC Radio. The new ones are already in operation, but they have different URLs. That fact is easy to find on the BBC web site. But what are those new URLs? I didn't succeed in finding them on the BBC web site. If they are there, they are well hidden.
You can connect to sites that already use them, such as TuneIn, and look at what they connect you to. That's what I did. Other people have done so, too. E.g., ‘Bpsib’ published a a list of BBC Radio streaming URLs with many more stations than my list below.
So, to help others, here are the URLs that work as of 10 March 2021.
They point to playlist files, i.e., they are not the MP3 streams themselves, but contain the URLs that are. Presumably, that is so that the stream URL can eventually change, but the URL of the playlist continues to work.
The playlists are in the .pls format. Not all media players understand .pls files, and some browsers don't either. If yours doesn't, you can still download the .pls file and look inside what the actual stream URL is. For convenience, the third column of the table below shows that URL. (Examples of media players that can play the playlist URLs directly are VLC and Apple's Music. The browser Safari also plays them. But to listen to the stream in Firefox or Vivaldi, you need the URL of the MP3 stream.)