Anonymous aggregates
I cannot imagine that lay people, i.e. politicians and journalists, will ever understand the difference between aggregated data and anonymous data.
Aggregated data would say, for example, the average blood pressure in postal area GU99 is P with standard deviation (*) Q. 'Anonymised' data says that Mr Z of GU99 9ZZ has blood pressure P. When the marketing droids also establish that Mr Z drives a red car and owns five computers, it all becomes uncomfortable.
It would be nice if database queries were restricted to aggregate data, but I don't see that as practical.
(*) Another term I have yet to see any journalist or poitician understand.