Curiouser and curiouser!
Well, I've solved my immediate web browsing problem with an hitherto unknown FireFox configuration variable, network.dns.ipv4OnlyDomains, which can hold a list of domains that will only be processed via the IPv4 stack.
Some further research led me to a FF bug report (bug 68796
https://bugzilla.mozilla.org/show_bug.cgi?id=68796), entitled "IPv6 : Some IPv4 addresses won't resolve w/IPv6 OS", with multi-YEARS worth of discussion on the matter/problem.
I've mucked around a lot with various DNS queries trying to find any hole, but haven't found anything definitive. Then again I tried a query that I must've tried several times with troublesome results:
dig aaaa @ns1.theregister.co.uk theregister.co.uk
The query just sat there awaiting a time-out; it presumably couldn't find ns1.theregister.co.uk.
So, I queried directly for the nameserver:
dig ns1.theregister.co.uk which responded with: 89.234.28.100
Then I retried the first query:
dig aaaa @89.234.28.100 theregister.co.uk and got the expected reply of NOERROR and NO AAAA record.
These queries were to the HE.NET server at 2001:470:20::2.
BUT, this doesn't happen all the time; is this some sort of caching issue?
In any case, I do have a quick solution for my FF browsing, but I suspect that there's something I'm incorrect with the DNS configuration for the theregister.co.uk servers.
Finally, the FF solution doesn't begin to address why the browsers Opera, Konqueror and Elinks also exhibit a similar problem with the website in question, though Dillo does not and works fine.