The group is led by Richard Lloyd, former executive director of the UK consumer group Which?.
The group estimates that more than five million iPhone users in the UK could be owed hundreds of pounds each in compensation from Google for the unauthorised snooping.
The class action alleges that between June 2011 and February 2012, Google bypassed the security settings on the iPhone's Safari browser and set a third-party cookie.
Which? chief executive Peter Vicary-Smith said: "People have to put their trust in big companies such as Google because they increasingly play a large role in our everyday lives. To have this good faith rewarded by Google taking advantage of people’s information without their consent is something that rightly must be challenged.
"This welcome campaign should empower consumers by bringing the issue into the spotlight and enabling those affected to rightly seek collective compensation."