Five Live's sports shows helped it reach record ratings
The number of people listening to BBC Radio each week has risen by 300,000 since September, taking the total to 32.7 million - a record since new monitoring methods were introduced in 1999.
BBC Radio 2 increased its grip as the most popular station in the UK, with 12.3 million listeners per week - a rise of 1.6 million in the last year.
Terry Wogan's show for the station, the most popular breakfast show among adults, reached a record audience level with 7.2 million people tuning in every week.
"I am delighted that Radio 2 continues to soar but the record performance of all our speech networks, and our local stations, demonstrates that in troubled times people turn to the BBC for news," said BBC Director of Radio and Music Jenny Abramsky.
BBC Radio 4 also had its best three months since 1999, with 10 million listeners, as did Radio Five Live, with 6.2 million per week.
"Radio Five Live has also had a phenomenal quarter for its sports coverage," Ms Abramsky said.
BBC Radio 1 is still in decline, though, losing 400,000 listeners over the last three months to take it to a level of 10.8 million listeners per week.
Commercial stations had a combined total of 31.9 million per week, according to the figures from Radio Joint Audience Research (Rajar).
Classic FM accounted for 6.7 million, while TalkSPORT has achieved its highest-ever audience figures, with 2.4 million listeners.
London's Capital FM's figures rose slightly to 2.95 million, while 100.7 Heart FM and Galaxy 105 consolidated their positions as the top two stations outside London.
Listeners tuned in for an average of 24.7 hours per week in the 14 weeks to 16 December, down slightly from 24.8 hours in the 12 weeks to September 16.