They have both been nominated for the comedy category of the Sony Awards: Iannucci for his Charm Offensive and Brigstocke for his world cup shows Giles Wemmbley-Hogg Geht Zum FussballWeltmeisterschaft Weg!
They are up against fellow Radio 4 show 1966 And All That, based on Craig Brown’s spoof history, Radio Scotland’s North By North North, and Martin Kelner’s fake interview show Pleased To Meet You, which aired on Radio Leeds and BBC 7.
The awards - the 25th - will be announced in London on 30 April.
Frank Skinner and David Baddiel's World Cup podcasts are in the running for the first Sony Award to be awarded for internet programming.
And Chris Evans, Jonathan Ross, Jamie Theakston and Chris Moyles are up for personality of the year.
