What are they recording?

There seems to be some confusion as to whether ISPs are recording all web page accesses for possible government (and third party interrogation) or not. This confusion certainly existed at the BBC yesterday as the article devoted to this story went through quite a few changes before this sentence was added at 16:02:52:

"Please note, in an earlier version of this story we incorrectly stated that ISPs would be storing details of website visits. This is not the case. "

So what, definitively, is the case?