Gregory's Server@losttourist @ben @BBCRD @JBsWhatsOn6 At least the BBC stations do post whats-playing to last.fm, then bots can use the API there. And RSS is available from Mastodon; just add /rss to the username eg https://dizl.de/@JBsWhatsOn6.rss and load that in your favourite RSS reader!
@johnb_rox @ben @BBCRD @JBsWhatsOn6 The Mastodon account whose RSS feed you linked is not a BBC account and in theory could be subject to a BBC cease-and-desist request although I doubt they'd ever do that.
But really it should be the BBC themselves, as the source of the information, who ought to be providing an RSS feed or other way to officially obtain the data.