@pfefferle I accidentally stumbled on the problem. I tried to ping another site I run from node.lordmatt.co.uk. That too gave the same reply.
So I took a look at the backend of node.lordmatt.co.uk. That's when I saw a notice about an expired anti-spam license. Disabled plugin. Everything works again.
I'd assumed it was WebMention as that's where the error was. Only now do I recall that 500s were recently changed to 403s. 4.5 hours spent re-learning to look at the simple stuff first.