In an ideal world, the data will only be accessed when there is a justification for it, and when access is required.
I was just reading about the terrible story of the low-life who left his son to die in a hot car in the US. It is an open and shut case, and some of the evidence that led to his conviction included nude photographs he sent at the time to some women, and an underage girl. Other evidence included Google searches on "How long does it take a child to die in a hot car" and something else (I have forgotten what).
This is an example of how the data used can help to convict people of crimes where, perhaps, it would have been difficult to prove that the child didn't die as a result of forgetfulness. If this is what the UK agencies are going to use the data for, then fair enough.
However, as I have pointed out, it is quite easy to misinterpret anyone's internet history to make them appear to be sick individuals who could be guilty of committing whatever crimes they need solved.
Also, it is possible that this data will get hacked, or go missing, or end up in the wrong hands.
If there is a potential that this data could be used to, say, jail an innocent person or to misrepresent a person - then I am absolutely opposed to it. Is "whofan" confident that the data being held cannot be misused at all?