Consumer rights group Which? is suing Apple for £3bn over the way it deploys the iCloud.
If the lawsuit succeeds, around 40 million Apple customers in the UK could be entitled to a payout.
The lawsuit claims Apple, which controls iOS operating systems, has breached UK competition law by giving its iCloud storage preferential treatment, effectively "trapping" customers with Apple devices into using it.
It also claims the company overcharged those customers by stifling competition.
The rights group alleges Apple encouraged users to sign up to iCloud for storage of photos, videos and other data while simultaneously making it difficult to use alternative providers.
Which? says Apple doesn't allow customers to store or back-up all of their phone's data with a third-party provider, arguing this violates competition law.
The consumer rights group says once iOS users have signed up to iCloud, they then have to pay for the service once their photos, notes, messages and other data go over the free 5GB limit.
"By bringing this claim, Which? is showing big corporations like Apple that they cannot rip off UK consumers without facing repercussions," said Which?'s chief executive Anabel Hoult.
"Taking this legal action means we can help consumers to get the redress that they are owed, deter similar behaviour in the future and create a better, more competitive market."
Apple 'rejects' claims and will defend itself
Apple "rejects" the idea its customers are tied to using iCloud and told Sky News it would "vigorously" defend itself.
"Apple believes in providing our customers with choices," a spokesperson said.
"Our users are not required to use iCloud, and many rely on a wide range of third-party alternatives for data storage. In addition, we work hard to make data transfer as easy as possible - whether it's to iCloud or another service.
"We reject any suggestion that our iCloud practices are anti-competitive and will vigorously defend against any legal claim otherwise."
It also said nearly half of its customers don't use iCloud and its pricing is inline with other cloud storage providers.
How much could UK Apple customers receive if lawsuit succeeds?
The lawsuit will represent all UK Apple customers that have used iCloud services since 1 October 2015 - any that don't want to be included will need to opt out.
However, if consumers live abroad but are otherwise eligible - for example because they lived in UK and used the iCloud but then moved away - they can also opt in.
The consumer rights group estimates that individual consumers could be owed an average of £70, depending on how long they have been paying for the services during that period.
Apple is facing a similar lawsuit in the US, where the US Department of Justice is accusing the company of locking down its iPhone ecosystem to build a monopoly.
Apple said the lawsuit is "wrong on the facts and the law" and that it will vigorously defend against it.
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Big tech's battles
This is the latest in a line of challenges big tech companies like Apple, Google and Samsung have faced around anti-competitive practices.
Most notably, a landmark case in the US earlier this year saw a judge rule that Google holds an illegal monopoly over the internet search market.
The company is now facing a second antitrust lawsuit, and may be forced to break up parts of its business.
Read more: Google faces threat of being broken up
And in December last year, a judge declared Google's Android app store a monopoly in a case brought by a private gaming company.
"Now that five companies control the whole of the internet economy, there's a real need for people to fight back and to really put pressure on the government," William Fitzgerald, from tech campaigning organisation The Worker Agency, told Sky News.
"That's why we have governments; to hold corporations accountable, to actually enforce laws."
(c) Sky News 2024: Apple sued by Which? over iCloud use - with potential payout for 40 million UK customers
