How 'bout Right Said Fred? (can't believe it hasn't been mentioned yet!)
Some of Cyril Tawney's stuff is funny: Five foot Flirt comes to mind, and On a Monday Morning has at least a couple of very funny lines...
As for trad songs -- there's I Wish They'd Do it Now, Mary Ann (is after me...), Bonny Black Hare, and then there are all the song(s) about the mole catcher/piano tuner/clock repairman and the policeman/banker/whoever's wife -- to name just a few...