This was the worst part of moving my site so far. Fiddling with DNS settings reminded me of when I used to be a freelance web designer, and I would offer hosting services to clients.
Anyway, after flicking a few switches in somewhat random order, I’d got the sequence correct and the domain switched away from GitHub and over to Netlify pretty quickly. I may have muttered “hold onto your butts” under my breath.
First I had to login to my domain name provider’s website and update the DNS settings for my domain (benjystanton.co.uk) to match the settings given by Netlify. This page in the Netlify docs helped me figure that out.
I also had to stop GitHub Pages from building my site and publishing it on my custom domain. This all felt a bit hacky, I had to switch the build to a new branch, then delete that branch. This GitHub docs page helped with that bit.
Despite feeling in over my head, the whole thing only took half an hour probably. And now my site is being hosted on Netlify.