After a very long call with a Senior iOS advisor at Apple I think we've found the the solution to a lot of Apple Music issues.
This worked for me, hopefully it will for you as well -
Remember you will lose anything music related in your phone. Just a warning to you before going any further.
Close Music
Then
Settings - iTunes & App Store and logout of your Apple ID.
Then
Settings - General - Usage - Manage Storage - and remove any Music.
Then
Restart iPhone
Double check that you don't have any playlists, downloaded music on your iPhone. If you do, then restart again.
Now -
Sign back into iTunes & App Store,
Then
Apple Music and turn on iCloud Music Library
Then
Open Music, and wait for your music and playlists to sync.
I'll be interested in knowing if this worked for anyone else.