First off, I never expect to see pudding widely used in U.S. to mean “dessert,” both because dessert is too entrenched and because pudding has a such a specific meaning here (“a thick, soft dessert, typically containing flour or some other thickener, milk, eggs, a flavoring, and sweetener”–dictionary.com).
That said, there is room (as is always the case) for ironic, self-conscious use, as Jason Diamond (@imjasondiamond) just observed on Twitter:
I confess I didn’t get the reference (never fancied Pink Floyd) so had to consult Wikipedia, where I found this under the entry for the song “Another Brick in the Wall”:
The song also features a group of school children for lead vocals in the second verse: as the song ends, the sounds of a school yard are heard, along with the teacher (portrayed as a Scotsman) who continues to lord it over the children’s lives by shouting such things as “Wrong! Do it again!”, and “If you don’t eat yer meat, you can’t have any pudding! How can you have any pudding if you don’t eat yer meat?!”, and “You! Yes! You behind the bikesheds! Stand still, laddie!”, all of it dissolving into the dull drone of a phone ringing and ending with a deep sigh
notoneoffbritishisms.com 
Jason you’re pretty dang funny! Thanks for the jolly good tweet.
Ben – you never “fancied” the Floyd? Oh dear oh dear. ;-D
I have only one thing to say to Jason. Shine on you crazy Diamond.
Which prominent Scottish politician is known as ‘Great puddin o’ the Chieftain race’? With apologies to Robbie Burns.
I think we discussed this when we were talking about ‘afters’. I don’t think most Brits limit their idea of pudding to “a thick, soft dessert, typically containing flour or some other thickener, milk, eggs, a flavoring, and sweetener” (which you got from an American dictionary) – for many of us pudding is simply informal for ‘dessert’. At home you have pudding (or maybe afters), in a restaurant you have dessert.
Try a British dictionary. Yes, Oxford Concise does include:
“cooked sweet dish served after the main course of a meal – a rice pudding”
but also:
“the dessert course of a meal – what’s for pudding?”
It’s the only Pink Floyd song that ever interested me, and I find that particular line irresistible. My kids were still in the highchair when they figured out the cause-and-effect relationship between their meat and their pudding.
Funny, I caught the reference immediately (big Pink Floyd fan), but I never knew that “pudding” was a general term for dessert in Britain. I have to admit I’ve used the line a few times when my kids weren’t interested in their main course. They weren’t amused.
Ben:
I agree with you; I doubt if “pudding” will ever get a Green Card, but who knows? The proof is in the pudding.
Ah, “The proof is in the pudding”. When I was a lad, the proof of the pudding was in the eating. How things change.
confusingly, pudding can also refer to savory dishes, for example: black pudding, a type of sausage made from pigs blood and oats… mmm!
I grew up with the word pudding as a general reference to dessert. ‘Pudding’ is a great comfort word for me. I’d bet that if I use ‘pudding’ in place of ‘dessert’ among my friends now they’d all laugh but it would evoke similar memories for them too. The Pink Floyd reference is a good one.
Please don’t forget Yorkshire pudding, or batter pudding which can either be sweet or savoury. Also steak and kidney pudding, which is made by lining a bowl with a suet crust, filling it with steak and kidney, topping it with suet, sealing the top and steaming for at least two hours (depending on the size). You can make sweet versions of this too – e.g. Sussex Pond Pudding which is filled with muscovado sugar and a whole lemon.
(never fancied Pink Floyd)
I’m guessing that’s an attempted Britishism? No Briton would say “Never fancied Pink Floyd”, they’d say they “never liked them”. “Fancied” sounds like something Dick Van Dyke might say.