A group of 12 people, all of whom use Apple devices, are seeking damages from the internet giant after claiming that their browsing habits were secretly tracked.
It is thought the case, being brought against Google by law firm Olswang on behalf of the internet users, is the first of its kind in the UK.
Cookies are used by advertisers, and owners of other websites, to target
Claimants thought that cookies would be blocked because of assurances given by Google in the time their devices were allegedly affected, from summer 2011 to spring 2012, and also because of Safari's default settings.
Dan Tench, a partner at Olswang, said: "Google has a responsibility to consumers and should be accountable for the trust placed in them.
"We hope that they will take this opportunity to give Safari users a proper explanation about what happened, to apologize and, where appropriate, compensate the victims of their intrusion."
Judith Vidal-Hall, former editor of magazine Index on Censorship, has issued proceedings against Google after claiming they had covertly tracked her use of the internet.
The 74-year-old said: "Google claims it does not collect personal data but doesn't say who decides what information is 'personal'.
"Whether something is private or not should be up to the internet surfer, not Google. We are best placed to decide, not them."
A campaigning group, called Safari Users Against Google's Secret Tracking, has been set up on Facebook and Olswang believes it could prompt others to come forward to take action. It is estimated there were 10 million users of
Google was fined $22.5m (£14.2m) in the US in late 2012 for using tracking cookies on Safari.
Mr Tench described the matter as being "concerning", especially because of the size of the company involved.
He said: "One of the things about this case is the ubiquity of Google. It is ever-present in our lives.
"The fact that they are the ones who have acted in this way is a matter of concern."
He said claimants were entitled to an explanation about what had happened and how their personal information was used.
A Google spokesman said they were unable to comment.
Nick Pickles, director of civil liberties campaign group Big Brother Watch, said: "This episode was no accident.
"Google tracked people when they had explicitly said they did not want to be tracked, so it's no surprise to see consumers who believe their privacy had been steamrollered by corporate greed seeking redress through the courts.
"This case could set a hugely important legal precedent and help consumers defend their privacy against profit-led decisions to ignore people's rights."