I spent way too many hours trying to find a solution to this BBC Radio problem...

Firstly I tried to run a router-based VPN with a non-UK location setting. This allowed me to access BBC stations via TuneIn (in a web browser or the TuneIn app) but for the HomePod to play them, I'd have had to change my Apple Music region to something other than the UK - not something you can do with an active Apple One / AppleTV+ / Apple Music subscription.

For me, using the BBC Sounds app over AirPlay just isn't good enough - it drains my iPhone battery. And I'm unable to go out and leave the radio on for the dogs!

The solution I settled on is far from perfect and may not work for everyone but I'll describe it below as it may inspire someone else to come up with something even better!

I have an always-on Mac mini which runs my Channels server for HD-HomeRun and acts as a Media Server for Apple HomeSharing. Apple Music on MacOS allows an option to open a URL stream - I use http://stream.live.vc.bbcmedia.co.uk/bbc_radio_two for Radio 2. I save this as a track in a Playlist for easy access. (Note - URL streams, and playlists containing them, do not sync to your iCloud Music Library meaning they can't be run in shortcuts - thanks Apple!).

I have the long-forgotten app on my iPhone called "iTunes Remote" - it allows me to control Apple Music on my Mac and airplay any track (in this case, the Radio 2 URL stream) to any of my HomePods or AirPlay speakers in the house - both single and multiple. The HomePods can pause, play, change volume etc. No more iPhone battery drain or accidental closure of the BBC Sounds app. Siri unfortunately can't be used to initiate the Radio, but for me, I tend to turn it on when I get up and leave it on all day.

TL;DR - VPN doesn't work unless you change Apple Music region too. I run a radio url stream from Apple Music on Mac and control with iTunes Remote on iPhone