Nick Grimshaw's Radio 1 Breakfast Show is the most popular live show among users, while Radio 4's I'm Sorry I Haven't A Clue is the most listened-to on-demand programme.
The BBC revealed that on-demand listening peaks during evening, with Radio 1's dance music show hosted by Annie Mac and Pete Tong performing strongly.
Radio 4's average live listener figures overtake Radio 1 after 10pm thanks to the popularity of programmes such as Book at Bedtime.
"With over one million downloads of the app and record-breaking audiences to BBC iPlayer Radio, we are thrilled that more and more listeners can take BBC Radio with them whenever and wherever they want," said BBC Future Media's Andrew Scott.
"We're looking forward to bringing even more exciting features over the coming months, and to launching the app on other mobile platforms in 2013."
The BBC has rolled out numerous updates for the iOS iPlayer Radio app since launch, introducing iPhone 5 optimisation and other features. The application will be released for Android devices in 2013.