Twelve people are seeking damages from the company for allegedly tracking their use of the web without their knowledge.
The claimants say Google designed a code to secretly install cookies - small tracking files - on the Safari internet browser.
Cookies can be used to target advertising based on the type of websites someone looks at.
Olswang, the law firm handling the case, gives the example of a person searching for engagement rings could find that their partner, using the same computer, later sees adverts for rings.
The claimants say they thought cookies were being blocked on the devices because of assurances given by Google and Safari's only default privacy settings.
It is estimated that around 10 million people could have grounds to bring a claim given the number of Apple users at the time in question - summer 2011 to spring 2012.
There is no suggestion that Apple is in any way at fault in the case.
Campaigners have also set up a Facebook "information" group called Safari Users Against Google's Secret Tracking.
Dan Tench, a partner at Olswang, said Google had a "responsibility to consumers and should be accountable".
He added: "We hope that they will take this opportunity to give Safari users a proper explanation about what happened, to apologise and, where appropriate, compensate the victims of their intrusion."
Google was fined $22.5m (£14.3) in the US last year over similar claims, with the Federal Trade Commission ruling that the firm had broken a promise not to mislead consumers over its privacy practices.
The company declined to comment on the matter when contacted by Sky News.
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