Thanks, InfluenceJamie, but I was — at the time of posting — getting a PDF, not web help. And I don't know how to restore web help.
OK, after some more digging…
Somewhere in my history of using Illustrator I've managed to switch to accessing a local PDF instead of the web-based help system — which (in its latest incarnation) is what you have linked to.
The PDF file is called "illustrator_reference.pdf", and (on my Mac) it lives in Users > Shared > Documents > Adobe > PDF > pdf.
I've just found the latest version of it online here: http://helpx.adobe.com/pdf/illustrator_reference.pdf— which has let me update the file to CC.
To see if I can return to the web based system I have tried deleting the Adobe folder mentioned above. Attempting to access Illustrator Help after that produces a dialog box that tells me I must be connected to the internet (which, of course, I am).
Restoring the Adobe folder and deleting only the PDF folder within it (leaving the other folder, entitled "Help") produces the same dialog. So I've restored the PDF folder as well.
The upshot is that I now have up to date help in PDF format on my local drive but no idea how to revert to Web help.