For me TuneIn was always a bit patchy - sometimes worked well for weeks on end and sometimes very glitchy.
My echos seemed to self-switch over the bbc player a week ago like everybody else but I'm finding that the stream isn't as reliable as TuneIn. Often just goes away after about an hour or so. I've deleted the skill for now as I think Tunein was better.
Another odd glitch with the BBC skill I found is that you couldn't change the volume until the stream was playing properly.........ie occasionally I wake up in the morning and say "alexa play radio 4" and then alexa responds at high volume (which I'd left it set to the previous night) ....so I immediately say "alexa volume down" ...and this then stops the stream. It's fine if you let it do the "chimes" and the "bbc announcement" then ask for the volume to be lowered. I't's just that you have to let it deafen you for short time....not good at 6:00am
First world problems I know
but Tunein just seems more integrated.