The case had previously been blocked by the High Court.
It was brought by Richard Lloyd, former director of the consumer rights group Which?
Google said in response: "The case relates to events that took place nearly a decade ago and that we addressed at the time."
"We believe it has no merit and should be dismissed," it added.
Between 2011 and 2012, Google cookies - small computer text files - collected data on health, race, ethnicity, sexuality and finance, through Apple's Safari web browser, even when users had chosen a "Do not track" privacy setting, Mr Lloyd alleges.
It is the first time a so-called class action - where one person represents others with the same complaint - has been brought in the UK against a big technology company over alleged misuse of data.
But the case was thrown out in October 2018 because the judge, Mr Justice Warby, said it was difficult to calculate exactly how many people had been affected and claims they had suffered damage were not supported by the group bringing the case.