Actually, that depends on what part of the world you're talking about. Pinatas have a very long and widespread history, being thought to have originated in China (which makes sense, given it's the birthplace of paper). In the 14th century, Marco Polo supposedly brought the idea for the pinata back to Italy, and the tradition subsequently became associated with the Christian celebration of Lent. Pinatas gradually made their way to Spain, where clay pots called "la olla" were decorated with paper and ribbons to make the pot more festive. They eventually became most popular in New Spain (what we now call Mexico), where they retained their highly religious connotation until more recently; today they're used for a number of celebrations and have evolved from clay pots to papier-mache.
The pinata featured in-game appears to be of the Mexican variety, rather than the Spanish kind, which leads to the question of how it got to Britain in the first place. My best guess would be through American influence, as suggested earlier in this thread; there's some great pictures from '61 of "Girls striking a pinata in a California carport," showing that the tradition had in fact made its way north of the border by around that time. It seems likely that the "powers that be" in the WHF universe have access to materials and information not readily available to the general public, possibly including knowledge on the state of things across the pond. They are therefore free to trickle as much of it as they like to the rest of society, as good 'ol Uncle Jack has done. He doesn't even have to be terribly accurate about it, and people are still likely to lap the whole thing up, even without the drugs (hell, the BBC ran an April Fool's prank in '57 that convinced far more people than it should have that spaghetti is grown on trees!).
In the end, though, regardless of accuracy, I think the whole sequence is perfect for its shock value and what it brings to the narrative as a whole, which to me is what matters most. Feel free to disagree if you like - I'm no expert...
Long post is long. Please excuse my rambling. Kthnxbai