Sounds a bit weird. If you tap on track one “Vivian Comma” does it not start that track and load the rest of the album into the queue? 

@Jimbobs999,

I see you have a VPN connection open on your mobile controller, what happens if you switch off that connection?

No - just plays the one song and stops. 
 

Fully exit the controller (swipe away from the background apps). Disable the VPN as suggested. Restart the controller. 

Further weirdness. If I use the search function to find the album, rather than going through the saved ‘albums’ link, then the ‘play’ button reappears:

VPN disabled, phone turned off and on again for good measure. Problem persists. 

So does the pattern repeat for other albums in the ‘saved’ list? (I don’t bother with Amazon Music Unlimited.)

It repeats with other albums - some have the magic ‘play’ button and some don’t. There doesn’t seem to be a discernible pattern. However it is always the same albums that have the missing ‘play’. 
 

I do use Amazon Unlimited, but have never seen the issue on my controller devices - maybe try an ‘App reset’ from "settings/app preferences” area. On reopening the App click through the usual opening screens and choose to connect back to the ‘existing system’. See if that fixes it.

Ok, so the problem also exits on my wife’s android phone and when using the Sonos app on my Mac. Does this mean it’s something to do with the Sonos / Amazon Music link, rather than to do with our devices?

You could maybe try removing/reinstalling the Amazon Music Service from the Sonos App/System to see if that resolves it. 

It perhaps might also be something on the local network that’s causing it - some kind of security/antivirus/firewall software on the router, or controller devices, perhaps - those were my other thoughts. It’s not something I’ve seen before with the controller App.