On what grounds could one sue?
Probably under data privacy laws.
I imagine it would be quite hard to prove real damages with a price-tag attached.
They don't need to show financial hardship:
Google argued the point was moot because consumers suffered no financial hardship due to the practice. The UK's Court of Appeal disagreed. According to the court's judgment:
"These claims raise serious issues which merit a trial. They concern what is alleged to have been the secret and blanket tracking and collation of information, often of an extremely private nature [...] about and associated with the claimants' Internet use, and the subsequent use of that information for about nine months. The case relates to the anxiety and distress this intrusion upon autonomy has caused."