Thanks to everyone who gave me opinions (both online and offline) following the demise of my old panniers. Last weekend the Co-Pilot and I went off to our favourite not-quite-local bike shop and had a chat to Bruce about possible replacements. In the end we walked away with a pair of Axiom "Stormfront" waterproof panniers.
I finally cracked them out and fitted them up to the rack this morning — after getting the wire-cutters out to remove the old one!
So far, so good. They're probably not as tall as I'd prefer (but that's a good thing, limiting the amount of crap I can load into them). They're similar to the Ortlieb waterproof bags with welded seams and the roll-and-clip closure. Unlike the Ortlieb there is a pocket on the flap, which I reckon is handy and the design shouldn't compromise waterproofing of the main compartment. Materials and construction seem to be pretty good quality although some aspects of the design aren't quite as neat as the Ortlieb. Overall it looks like a reasonable balance of cost and benefit.
Anyway, we'll see how they go. Hopefully it'll be many years before I have to report the sad demise of another pannier.