How do I switch wifi network on my HomePod?

I switched broadband provider and needed to change the wifi for the HomePod. Answers on here were pretty negative and, along with Apple, seemed to suggest a 'Reset to Factory Settings' and re-install the HomePod. Yeuch. But I tried a different approach and it was really simple.

Instead, I plugged in the new router and updated my iPhone and MacBook to the new wifi. Then I unplugged all the routers and mesh kit with the old wifi. They need to be unplugged so that they're not broadcasting the old wifi name - even if it's a "dead-end" signal. Switch off the HomePod for five minutes. Switch it back on again with my iPhone next to it. And it worked.