I’ve resolved this problem. I found this in the Akismet FAQ.
My API key doesn’t work!
We get this pretty often, try these steps:
* Try the key again, after a few minutes.
* Type in the key instead of copying and pasting it.
* Ensure that your host can make outgoing HTTP requests to akismet.com. (Many hosts block or firewall outgoing connections.)
I dropped an email to my host explaining the situation and asked if they were blocking outgoing requests. They said they were, but they’ve opened requests to akismet.com for me, and it worked straight away!