Lawyers representing Apple said in a notice filed with the Competition Appeal Tribunal on Friday that the Competition and Markets Authority's investigation should be reviewed.
In its argument, lawyers said that the CMA had missed timing requirements linked to the launch of an investigation.
"Apple seeks 1) an Order that the MIR Decision is quashed. 2) a declaration that the MIR Decision and market investigation purportedly launched by reference to it are invalid and of no legal effect," the filing with the Appeal Tribunal showed.
Responding to the appeal, the CMA said on Friday it would defend its position and continue to progress its work in line with the statutory timetable.
"We opened this investigation to make sure that UK consumers get a better choice of mobile web services and that UK developers can invest in innovative mobile content and services," the CMA said in an emailed statement.
Last November, the CMA, Britain's competition regulator, launched a full investigation into cloud gaming and mobile browsers on concerns about restrictions by iPhone-maker Apple and Google.
There is due to be a preliminary hearing on the matter on Tuesday, according to the Competition Appeal Tribunal website.