Data protected by Apple's standard level of encryption is still accessible by the company if a warrant is issued, but the firm cannot view or share data encrypted using its toughest privacy tool, Advanced Data Protection (ADP).
ADP is an opt-in feature and it is not known how many people use it.
Last week, Apple chose to remove ADP from the UK market rather than comply with the notice, which would involve creating a "backdoor" in the tool to create access.
Apple said at the time that it would never compromise its security features and it was disappointed at having to take the action in the UK.
The UK's order also angered the US administration with President Donald Trump describing it to The Spectator as "something that you hear about with China".
Tulsi Gabbard, US head of intelligence, said she had not been informed in advance about the UK's demand.
She wrote in a letter that it was an "egregious violation" of US citizens' rights to privacy and added that she intended to find out whether it breached the terms of a legal data agreement between the US and the UK.
The FT, which first revealed Apple's legal action, reports that the tribunal case could be heard in the next few weeks, but may not be made public.
The Home Office refused to confirm or deny that the notice issued in January exists. Legally, this order cannot be made public.
But a spokesperson said: "More broadly, the UK has a longstanding position of protecting our citizens from the very worst crimes, such as child sex abuse and terrorism, at the same time as protecting people's privacy.
"The UK has robust safeguards and independent oversight to protect privacy and privacy is only impacted on an exceptional basis, in relation to the most serious crimes and only when it is necessary and proportionate to do so."
Apple declined to comment.