British people of a certain age have an instinctive belief that music, documentaries, news and entertainment should be free and of good quality. This is because the BBC spoiled at least two or three generations by providing a lot of good music without advertising and without a subscription charge. The TV license is for broadcast television, there is still no charge for listening to the radio.
The BBC has to be navigated carefully, because you might fall into some Metropolitan Goodthink, and it takes a good few washes to get those stains out. As for the commercial stations, I can't stand advertisements, so commercial radio is a no-go. It didn't used to be, but it is now.
The full-bore streaming providers (Tidal, Qobuz, Deezer, Amazon Music, You Tube Music, Apple Music and some Swedish outfit) all charge. We're not looking at them right now. What can we get for free?
All the following have Apps and a website.
Radio Player provides access to a lot of UK radio stations, but not so many from outside the UK. If the stations use ads, you will get the ads.
Accuradio is a weird one. It has a wide range of channels, does have ads, and will lock you out if you listen for too long! The streaming rate is positively 1990's at 32kps (not a misprint).
There is TheClassicalStation(.org) which is conventional radio station based (or at least its phones are) in North Carolina. You get what they are broadcasting at the time, just like Radio 3.
Mixcloud (https://www.mixcloud.com/) has a wide selection of mixes and podcasts from DJs and programme makers. It's heavily oriented to dance / jazz / soul and similar, as the 'Mix' bit suggests. There are recognisable names using it, and the quality is generally good. If you don't like what you hear, just choose another mix. I am currently in the middle of a Mixcloud phase.
Bandcamp allows artists to upload music or podcasts, which can be listened to free, and if you like what you hear, you can
support the artist by buying the track or CD. I have purchased one piece from Bandcamp (Headnodic & Raashan Ahmad's
Low Fidelity, High Quality (Vol.2)). I got a think you e-mail and he got a darn sight more than he would from Spotify or a record label.
Soundcloud provides the same functionality as Bandcamp, though has more podcasts. "All podcasts are on Soundcloud" - except Joe Rogan. You can buy direct from the artist via Soundcloud.
Music Passion (aka Classical.com) looks like a classical music version of Bandcamp / Soundcloud, and has a $1/month subscription. (That's nearly free.)
Idagio is a classical streaming service which is free-with-ads, or ad-free and CD-quality with subscription. It looks a little mainstream to me: you're not going to be troubled by Boulex or Pendercki.
DanzWaves is an app with three radio streams: Chilltrax, Radio Danz, and Predanz. Chilltrax is what it suggests; Radio Danz has House and Dance music; Predanz has dance tracks from the 1990s and 2000s.
None of these will provide a guaranteed stream of listenable classical music at any time of the day or night. Not even Radio Three does that - the closest it gets is the Through The Night programme.
Which is a dodge I hadn't thought of. Go to https://www.bbc.co.uk/sounds/play/live:bbc_radio_three and scroll down for the Highlights. Night Tracks will provide you with perfectly acceptable music that lasts an hour or so.
If you want classical music, it may be all you need.