Radio 2's share of listeners was 17.7%, compared to 16.8% last year and 17.6% in the previous quarter.
On air this morning, Evans indirectly thanked his news presenter Moira Stuart for having helped to boost the show's reputation and in diffusing much of the flack surrounding news the presenter was going to takeover from national treasure Terry Wogan.
The furore surrounding the arrival of Evans on Radio 2 at the start of 2010 could provide some solace perhaps for his counterpart Radio 1 breakfast DJ, Nick Grimshaw, who has lost nearly a million listeners since taking over from Chris Moyles in September.
Radio 1 reached 10.26 million listeners a week, down 7.9% from 11.14 million this time last year and 11.09 million in the final quarter of 2012. Share was 6.7%, compared to 8.2% last year and 7.4% last quarter.
Grimshaw took over Radio 1's primetime breakfast show in September 2012 amid mounting criticism from commercial rivals and the BBC Trust that 38-year-old Moyles and his team were attracting an older audience than the station's target market.
Helen Boaden, director of BBC Radio, said: "Radio kicks off 2013 with a robust set of figures for the industry as a whole and I'm delighted that BBC Radio still attracts more than 35 million people every week. Radio 2 goes from strength to strength, setting new records across the board.
"The brand new schedule continues to bed in at Radio 1 and we remain confident that it will emerge strongly from a period of transition. Radio 1 is in good health – as clearly demonstrated by five golds at this week’s Sony Radio Academy Awards."
Elsewhere, Radio 4 scored a weekly reach of 10.76 million from 10.31 million last year – an increase of 4.4% – and stable over the quarter. Share was up to a record 12.8% from 11.9% last year and 12.5% last quarter.
The Today programme had a weekly reach of 6.94 million, up from 6.66 million last year but down slightly on the quarter from 7.05 million.
All four BBC digital networks continued to show strong performances with increases on the year.
The share of audiences listening to the radio on digital platforms was also up – to 34.3% from 29.2% last year and 33% last quarter. 6 Music had a weekly reach of 1.81 million, up 24.7% on last year’s 1.45 million but down slightly on 1.89 million last quarter.
1Xtra reached one million listeners a week, up on last year’s 916,000 and roughly in line with last quarter’s 1.04 million.
5live Sports Extra had a weekly reach of 860,000, down from last year’s 952,000 but up on 847,000 last quarter.
4 Extra was at 1.64 million listeners, up on 1.5 million last year and down slightly on 1.69 million last quarter.