All the system info is stored  on all speakers, so it is vital that you do not factory reset them both.  But I don’t think you need to factory reset anything and should avoid it if at all possible.  This may help guide you:

https://support.sonos.com/en-us/article/connect-sonos-to-a-new-router-or-wi-fi-network

Thanks John B for your response:

The Sonos docs eventually lead to no other option than to reset the Play:1 - after >hour waiting on the support line (more fool me) the agent confirmed I should do the factory reset.

So I did the following and (nobody more surprised than me), it worked ……. :

First, the ‘One SL’ 

Make sure your Sonos app (Android in my case) is connected to your new WiFi network.

When the app says ‘No Products Found’, or similar, follow the invite to update the network.

The system will only search for/find units compatible with Bluetooth (BLE) and so in my case this was just the single ‘One SL’

I followed the network update process more than once but the app persisted in saying ‘No Products Found’ so resorted to the usual last hope of turning the ‘One SL’ off and on again.

And it worked - the app showed me my system with the ‘One SL’ and ALL THE PLAYLISTS 

(I guess the old WiFi network configuration was somehow cached in the unit). 

Secondly the Play:1

Reset the unit as described here Factory reset your Sonos product | Sonos

When get the flashing green light (re)add the speaker to the system as described here Add a new product to an existing Sonos system | Sonos

All good - both units were visible to the system and working, all playlists and Spotify streaming service still shown/configured as before.