Today, I decided to get it sorted. I connected it up to via the network cable to run some diagnostic software and...it failed to connect to the internet. Eventually, I gave up and phoned the Telewest helpline. They refused to help since it was connected via a router, but offered me a number for a £1 a minute service. I declined and bypassed the router. My helper suggested lots of things to try. It still didn't work.
Much, much later, by which point I have had several attempts to reinstall the adaptor card, update drivers etc, I suddenly remembered the System Restore facility. I rolled it back to May, re-booted and ta-ra - it works! Still don't know what the problem was, but who cares?
Now why didn't the 'helpline' suggest that it in the first place? Grrrr!