Evans's Radio One Breakfast Show draws a weekly audience of more than 7 million listeners and is the most popular single radio show in the UK.
His success follows Mr Bannister's decision to axe several leading DJs and move veteran Steve Wright from the premier morning programme.
Last week Evans extended his Radio One contract, worth a reputed pounds 400,000, until the end of 1997. His programme was beaten into second place by rivals Russ and Jono of Virgin Radio in the music-based breakfast show category.
BBC Radio 5 Live's coverage of the Ryder Cup play-off between Philip Walton and Jay Haas last year received Gold awards for best sports programme and best event coverage.
There was further glory for the BBC as Dr Anthony Clare's interview with round-the-world walker Ffyona Campbell won the Interview of the Year trophy.
The Music Presenter of the Year award went to Radio 3's Brian Kay for his Sunday morning show.Reuse content