The alleged failings were revealed in the Cambridge Analytica scandal, where harvested data was used for advertising during elections.
Journalist Peter Jukes, leading the action, claims his data was compromised.
Facebook told BBC News there was “no evidence" UK or EU users’ data had been transferred to Cambridge Analytica.
But the case against the technology giant, expected to last for at least three years, will argue a “loss of control” over users' personal data warrants individual compensation.
The harvesting of Facebook users' personal information by third-party apps was at the centre of the Cambridge Analytica privacy scandal, exposed in 2018.
Cambridge Analytica's app on Facebook had harvested the data of people who interacted with it - and that of friends who had not given consent.
And the case is being represented by law firm Hausfield “on behalf of those Facebook friends”.
Mr Jukes said he wanted to ensure the situation could not arise again.
The action seeks damages from Facebook over failure to comply with the Data Protection Act 1998.
A Facebook spokesman said: "The Information Commissioner's Office investigation into these issues, which included seizing and interrogating Cambridge Analytica's servers, found no evidence that any UK or EU users' data was transferred by [app developer] Dr [Aleksandr] Kogan to Cambridge Analytica."
But Mr Jukes told BBC News it was not about “where the data went” but rather “that Facebook didn’t care".
"They didn't look after it,” he said.