Rupert Grint, George Michael and funnyman James Corden also feature in the skit, which shows the stars fighting over who should go to Africa as a celebrity ambassador for the organisation.
Corden volunteers - but McCartney tells the Gavin & Stacey star he's too fat for the trip, quipping: "People don't like seeing tubby people over in Africa. If they hadn't eaten so much, no one would be starving."
Beckham is also turned down as he "can't cry", while Keira is rejected from the mission for being "too gorgeous".
The annual Comic Relief fundraiser telethon will hit screens in Britain in March (11).