Call me cynical, but if this issue had affected a couple of dozen US radio stations instead of UK ones, it would have been fixed by now...
I've found that the issue with the Global Player stations is a real mixed bag. A number of stations can still be played by name - I've not been through every one of them but these are the ones I've tried that work simply by saying "Siri, play <station name>":
Capital (have to say "Capital radio" and then it plays a local variant of the station)
Capital Anthems
Capital Chill
Gold Radio
Smooth Relax (it played OK after part of the "sorry, there was a problem with Apple Music" message was announced)
Heart 80's
Heart Musicals
Radio X 90's
Classic FM Calm
These stations don't work by saying the name:
Capital Xtra
Capital Xtra Reloaded
Smooth (radio)
Classic FM
LBC
These ones worked when adding "via TuneIn" to the command:
Capital Dance (just asking for the station by name played some sort of playlist)
LBC News (just asking for the station by name played a podcast)
One that didn't seem to fit any of the patterns above was Smooth Chill - asking by name-only played something, but it wasn't from TuneIn and wasn't the Global Player radio station. Adding "via TuneIn" didn't make any difference
Getting fed up with the perceived lack of action now. AirPlay is clunky and awkward, and not acceptable as a long-term solution. I have lots of HomePod Minis scattered around the house, and when streaming via AirPlay I can't simply ask one of the HomePods to "play this in <room name>" as I move around the house. I get "Sorry, I can't do that when using AirPlay". The stream has to be redirected from the device I am AirPlaying from, which is not always in the same room I'm in at that moment, so I then have to trek around the house to find it. That might be OK in a small apartment, it's not so OK in a three-storey farmhouse when the device is in the lounge and I'm in an attic room.
@stephenseuk would it perhaps help if more of us bombarded Apple Support with complaints about this issue, to lend it some more weight?