A claim lodged with the High Court against parent company Google accuses the firm of collecting children’s data without parental consent.
Privacy expert Duncan McCann, who is bringing the action, argues this is a breach of UK and European (EU) law.
A YouTube spokesperson said it does not comment on pending litigation and the platform is not for use by under-13s.
Mr McCann, a father of three children under the age of 13, believes that if the case is successful, damages of between £100 and £500 could be payable to those whose data was breached.
“When the internet first emerged, we used to be worried about how children used the internet, said Mr McCann.
“That is still a problem, but now it’s a two-way street. We need to focus on how the internet is using our children, and ask ourselves if we’re comfortable with them becoming a product for these digital platforms?”
“That’s the future I don’t want,” he added.
He told the BBC that the class action is the first in Europe brought against a technology firm on behalf of children. He says that estimated damages of more than £2bn are being sought for about five million British children as well as their parents or guardians.
He will argue that YouTube and Google have breached the UK’s Data Protection Act and the EU’s General Data Protection Regulations.
The case will focus on children who have watched YouTube since May 2018, when the new Data Protection Act became law.
“I think we’re at the stage, where the only way we can move forward and hold these companies accountable is through the legal process,” Mr McCann said.
A YouTube spokesperson said: “We don’t comment on pending litigation. YouTube is not for children under the age of 13.
“We launched the YouTube Kids app as a dedicated destination for kids and have made further changes that allow us to better protect kids and families on YouTube,” they added.
The video platform has also previously said that it does not sell its users’ personal information to advertising companies.
The case is not expected before next autumn.
Mr McCann also told the BBC that it will also depend on the outcome of another data and privacy case being brought against Google.
Campaign group Foxglove and law firm Hausfeld have also said they would support Mr McCann’s case.