Advanced Data Protection is an opt-in feature that allows users to turn on a higher level of protection for data stored in iCloud, such as back-ups, Drive storage, photos and voice memos.
It is secured using end-to-end encryption - meaning not even Apple would be able to see its contents.
The government's requests for Apple to permit it access to data held under this system were issued under the Investigatory Powers Act (IPA).
It includes powers allowing the government to issue secret notices - called technical capability notices - which can secretly force companies to provide UK security services with ways to access customer data.
The government had fought unsuccessfully to keep legal challenges to its first notice to Apple secret.
Its notice was later withdrawn after angering US politicians, who were concerned it would affect their own citizen's data.
But the government issued a new request in October which did not apply to US users.
Privacy groups which previously campaigned against its secret orders welcomed Apple's new legal complaint.
"We are happy to learn that Apple is once again challenging the UK's regime of secret orders," said Privacy International.
"While we don't know the substance of Apple's claim, if it relates to the previously reported orders aimed at undermining the security of Apple's iCloud storage, then Apple's claim, alongside side ours and Liberty's, is crucially important to preserving all of our privacy and security."
Ruth Ehrlich, director of external relations at Liberty, said the case was "hugely important" and has "far-reaching implications for the public's privacy rights well into the future".
"End-to-end encryption is an essential security tool that protects our personal data, including our bank details, health information, private conversations and images," she said.
"Opening a backdoor to all of that information carries a wide range of risks to our personal data. It is critical that the Government listens to the many concerns and commits to protecting our privacy rights."
But Sir Brian Leveson, the Investigatory Powers Commissioner, who provides independent oversight of the use of surveillance powers, has previously criticised media use of the term "backdoor", external.
He said notices such as those concerned in this case would only be issued "if the Secretary of State deems it necessary and proportionate, and this decision is independently reviewed and approved by a Judicial Commissioner".
He added requests for data would also require separate authorisation under the IPA and these would be subject to independent oversight.

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