In the UK ISPs are required to keep logs of the domain name of every site you visit (e.g. “bbc.co.uk” if you visit any page on the BBC web site).
This might suggest that the logging is done by DNS servers. If that is the case, the simply changing to use alternative DNS server (e.g. OpenDNS) would avoid this monitoring. Of course, OpenDNS is itself an unknown quantity. I am looking for better alternatives.
It seems likely that this is how the monitoring works. The Cleanfeed censorship system works by matching IP addresses at edge routers and sending hits to a proxy server for testing of specific URLs. The overhead of trying to log actual HTTP accesses and then do a reverse DNS lookup would appear to be too high to make it realistic.