It sounds like the command isn’t reaching the system properly, or the activation isn’t being sent back to Sonos properly. Given that you have rebooted both the speakers and the router, I suspect your best bet is to submit a system diagnostic within 10 minutes of experiencing this problem, and call Sonos Support to discuss it.

There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution.

When you speak directly to the Support staff, they have tools at their disposal that will allow them to give you advice specific to your network and Sonos system.

Thanks Bruce will give that a go in the week when the support desk is open. 

I’d be interested to hear back what resolves the issue!

I have exactly the same issue …I can play bbc radio 4 through the Sonos app…but if I ask Alexa on my Sonos on she says she’s playing it …but no sound. Even if I “ask bbc sounds” I get the BBC sounds voice asking me what I want to listen to…and then I ask for radio 4 and again nothing comes out….mmmm

I got through to Sonos support, and we managed to fix this quite quickly. 
 

Try: Open the ALEXA App and disable the Sonos skill, and the BBC skill. Then re-enable both, and try again. 

Thanks for this…I did exact;y as you suggested and it’s all working now….brilliant.

Anyone having Alexa problems where all appears ok  and acknowledges request but won't implement. I discovered Alexa was connected to my Sons account which we share. Soon as I Said “Alexa switch to (my named account) all was well. Hope this helps others.