[Jayne Osborn]

Maryann said:
"I forgot to add that there are some well known weekly contests for humorous poems, run by British newspapers, that prohibit poems that have appeared in public anywhere. Sphere poets who enjoy those contests use a private board here that requires an extra login."

John,
Maryann was referring to competitions in The new Statesman, The Spectator and The Oldie rather than newspapers per se, as she mentioned Deep Drills as the place to find them.
(I don't buy newspapers but I think the answer to your question is probably 'none'.)

Jayne