Where is Charlie and the Chocolate Factory set?

The story opens in Charlie Bucket's house, which is described as "a small wooden house on the edge of a great town." Dahl says that it wasn't large enough for all seven people who lived there; there were two rooms and one bed. All four of Charlie's grandparents share the bed.

The house is comfortable in the summer but freezing in the winter. They're too poor to afford better lodgings because Charlie's father is the only one who works and he has to support seven people on his low-paid job as a toothpaste cap-screwer.

Charlie walks through his unnamed town every day fantasizing about chocolate. He stops at the chocolate shop to look at what they have to offer, though he can't afford it. It's there that he eventually buys the chocolate bar with the golden ticket. 

The primary setting in the novel is Wonka's Chocolate Factory. It's protected with large iron gates and a wall. From the outside, can hear strange whizzing sounds, see smoke rising from the chimneys, and smell chocolate from half a mile away. Charlie's family claims that it's the largest one in the world; they say it's fifty times as big as any other chocolate factory. 

When Charlie wins the contest and is allowed to go inside, he finds that the factory is a bizarre and exciting place—but also dangerous. There's a chocolate river; there's a room where everything is edible and chocolate is mixed by a waterfall. The factory has a mountain made of fudge, a lake of hot caramel, and a village of Oompa-Loompas. There's also a room that houses Television Chocolate where the chocolate "works by television" according to Willy Wonka. When a young boy tries to go into the television—which works as a transporter—he is shrunk down small enough to fit in his father's pocket.

When and where does Charlie and the Chocolate Factory take place?

We are not given a particular setting for this story. We are told that it takes place in a "great town:"

The whole of this family — the six grown-ups (count them) and little Charlie Bucket — live together in a small wooden house on the edge of a great town.

We also know that people like the Buckets live in poverty while others live in comfort, and the town is dominated by the chocolate factory.

We are also not given a particular date for the story. The book was published in 1964, and the story seems to take place around the year 1964, because of the modernity of the factory. For instance, the children take an elevator that zooms quickly and:

stopped and hung in mid-air, hovering like a helicopter

Since a comparison to a helicopter would only make sense in a story set after the helicopter had been invented, which was not until 1939, we would have to assume the story is, at the very least, supposed to be set post-1939.

However, Dahl does give his tale a universal, fairytale like quality.