The case is about balancing national security against privacy rights.
ADP is end to end encrypted, meaning no-one can access files that have been secured with it apart from their owner.
Other end to end encrypted services in the UK include Signal, Meta’s WhatsApp, and Apple’s iMessage.
In February, it emerged the UK government was seeking the right to be able to access data protected in this way using powers granted to it under the Investigatory Powers Act.
The Act allows it to compel firms to provide information to law enforcement agencies.
Apple responded by pulling ADP in the UK and then launching legal action to challenge the government’s demand.
Apple says agreeing to what the UK is asking for it would require the creation of a so-called backdoor, a capability critics say would eventually be exploited by hackers.
“As we have said many times before, we have never built a backdoor or master key to any of our products or services and we never will,” Apple says on its website, external.
The Home Office has previously told the BBC: “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.”