Oh yes, 6 Music is a good one. I notice that Iggy Pop has a Sunday afternoon show at the moment (16:00 UK time), and he’s had several series on there in the past, they just keep asking him back because he’s interesting and has good taste in music. And also on Sundays (20:00 UK time) is Stuart Maconie’s Freak Zone, which has been running for years - so long in fact that when it started I remember recording it on cassette tape so I could play it on my commute to work.
As with all BBC radio there are no adverts apart from their own promotional stuff, and everything is available for 28 days after broadcast via the BBC Sounds website and app - https://www.bbc.co.uk/sounds/stations
I spend a lot of time listening to BBC Radio 3, which is their classical station, but they also have a jazz show 5 nights a week, and lots of other music apart from classical - ‘world’ music, experimental and new music, all kinds of interesting stuff in the evenings UK time. Serious music radio, done properly.
There is a history of inclusive radio in the UK which goes back at least to the 1960s. Anyone who was born here and is over the age of about 50 will know about Kenneth Williams, who appeared in radio comedies with Hugh Paddick. The material is dated and may be regarded as clichéd and demeaning now, but they played two gay men called Julian and Sandy on a show called Round the Horne from 1965 to 1968, and the same characters came up in later shows as well. Bear in mind this was on national radio at a time when gay sex was still illegal in the UK. See https://en.wikipedia.org/wiki/Julian_and_Sandy for more details.