S1 or S2? Do you have other speakers that are connected, and how, wired, or wifi? Is this PLAY:1 wired to your router directly?  Was this PLAY:1 part of your system before hand, or did you get this from somewhere else? Have you tried to contact Sonos Support? Have you tried a factory reset of this PLAY:1? What devices and OS are you running your controller on?

Thank you very much for your response. To answer your questions:

1. ​​​​​​​I have had two Play 1 speakers for many years, operating with the S1 Controller on my PC (Windows 10) and Samsung phone. Both wifi-connected to my BT router. All was going well until just recently, when the system simply stopped working and I was unable to bring it back to life.
2. I have been in touch with Sonos Support and had a longish session with Eugen. He took me through some button-pressing exercises, which may or may not have been the factory reset process, and recommended that we proceed as if it were a new system.  The next step was to install the Sonos 2 controller and he sent me a link to use for this purpose. However, in navigating away from him and downloading this app, we were disconnected.
3. For this exercise I had wired speaker 1 directly to the router. Connecting speaker 2 would be the job of speaker 1, he said.

So I’m afraid I remain in limbo, and would much appreciate guidance.  …  Chris

Ok, so, we’re losing any previous playlists, and other data due to the the factory reset process you’ve done. And I assume you’ve not called back in to support, who would have the notes from Eugene in the system, and likely be able to pick up where you got disconnected. 

You should be running S2 on your mobile phone, ignoring the windows box for now. Open the S2 controller while speaker 1 is wired to your router with an Ethernet cable. I’m somewhat concerned that this is a BT router, there have been so many posts over the years about issues with them, but I’ll forge ahead anyway, and we should get you set up, hopefully,

When prompted, you should get (if memory serves) a ‘connect to existing system’ or ‘create new system’ , you’ll want to choose the latter. However, it’s possible you may not get this prompt, if the speakers have been factory reset. If you do, go ahead and choose ‘create a new system’, and follow the prompts to get the first speaker set up. 

Once that is done, you should be able to see that speaker in the controller on your phone. Use the ‘add a device’ prompt inside the controller to add speaker 2. 

Delete the S1 controller from your windows box, and download the S2 app from Sonos’ website, and open it. If prompted, select ‘join an existing system’, or words to that effect, and it should then connect to your two Sonos speakers.

At this point, you can enter in the Wi-Fi information into your phone controller if you want to eventually remove the cable connection between your router and your speaker. I recommend maintaining that connection, especially on a BT device, but it may be inconvenient to have your speaker so close to the router. If that’s the case, I’d recommend a BOOST (not a BRIDGE, they’re out of date, can’t run S2, and have dodgy power supplies at this age). But make sure there is at least a meter between any wired device and your router.

You may want to search these forums for BT, and read some of the other folks difficulties with their hardware. While I’m not in the UK, I use a separate router for my system, and use my ISP’s hardware as only a modem, turning off all ‘router’ functions, and using my own. 
 

Greetings!

On opening S2 : I get a message saying ‘Let’s finish adding Play 1 to your system.’  (I have previously opted to ‘create new system’. 

I then have to sign in to Sonos. ‘We’ll use this account to finish registering your sonos system’

Then: ‘Linking your Play 1 to your account’.   Then: ‘We couldn’t link your Play 1 to your account. Check your wifi and try again later.’

I press the Continue button and the same sequence repeats itself. Now including a suggestion to contact sonos support.

The problem can’t be wifi-related because the speaker is ethernet-cabled to the router.

Getting the first speaker set up is the challenge, but what’s the problem?!

As a guess, this speaker is still set up as an S1 speaker, but it’s hard to be sure. I’d really recommend calling back in to Sonos support so that they can continue the process where they left off, which should be in the notes Eugene left on your account. Plus, they have tools to see exactly what’s going on in your system, whereas I’m just imagining and guessing. 

Thank you for your time and for your help. I shall do as you suggest and hope for the best.

With best wishes for the New Year  …  Chris.