Apple Music's been broken for a while
It looks like something is very wrong with the DNS entries for Apple Music and a chunk of apple's back end.
Google's DNS (and Sky's DNS too) seem to be reporting the wrong hostnames for large swathes of Apple's estate. Apple themselves are telling people to use Norton Connectsafe DNS servers which do work (I was able to get Apple Music to work fine once I forced my home PC to use the Norton DNS servers rather Google (my usual default) or the standard Sky DNS that comes with the fibre service).
May well be something to do with Akamai - as it randomly works and randomly doesn't.
Not great for a service which, as you all will quote 'should just work'.
Well, it obviously just doesn't. :)