If the claim is successful, people who had an iPhone between 2011 and 2012 could receive up to £200 (R 3680.36) in compensation each.
Google is facing legal action launched on behalf of 5.4 million people in England and Wales over allegations it unlawfully collected their personal data.
If successful, those affected could receive compensation.
The company is alleged to have placed cookies on the Safari browser to track users.
Unusually, the campaign is a representative action, brought on behalf of all those affected – similar to a class action lawsuit in the US.
Richard Lloyd, the representative claimant in the case, told Sky News: “My job is to represent everyone that was affected by this breach of trust by Google to make sure that these vast companies have to be held accountable in the British courts.
“They’re not above the law. And we want to see more than five million British consumers given the compensation they’re due.”
The campaign estimates that, if the claim is successful, those affected could receive up to £200 (R 3680.36) in compensation each.
That would leave Google with a bill of more than £1bn.
A Google spokesperson told said: “This is not new – we have defended similar cases before. We don’t believe it has any merit and we will contest it.”
Google has previously paid millions to settle cases about the so-called Safari Workaround.
In 2012, it paid $22.5m to settle changes brought by the US Federal Trade Commission.
The following year, it paid $17m to 37 US states and the District of Columbia to settle claims.
In March 2015, the Court of Appeal in the UK ruled that consumers did have the right to sue Google in the UK over the alleged misuse of privacy settings.