6 Music, which was earmarked for closure in 2011 until the BBC Trust intervened, increased its weekly reach by 31% year-on-year to 1.89 million.
> Nick Grimshaw BBC Radio 1 Breakfast Show listening figures revealed
This is an increase from 1.62m last quarter and 1.44m in 2012.
Radio 2 had a reach of 15.1m listeners in the most recent quarter, an increase from 13.9m in the previous quarter and 14.3m last year.
The Chris Evans Breakfast Show reached 9.52m weekly listeners, up from 8.55m last quarter and 8.86m in 2012.
The station's share for the quarter rose from 15.6% last quarter and 16.3% in 2012 up to 17.6%.
"It's also good to see steady and in some cases spectacular growth in our digital networks and in digital listening across the industry."
The BBC Asian Network, which had been threatened with closure alongside 6 Music, had a reach of 453,000 listeners, down from 584,000 last quarter and 472,000 last year.