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Generally, UK retailers are free to set their own prices, and price controls don't exist.
The law requires sellers to show the full selling price, including VAT, of all products they sell to consumers. They must also show a unit price for products sold from bulk. This includes certain products marked with an indication of quantity or pre-packed in a constant quantity, and fresh fruit and vegetables (e.g. price per kilogram, litre etc.). For example, a bag of 10 oranges costing £5 might display the unit price as 50p per orange. These price indications must be unambiguous, easily identifiable, clearly legible and must include VAT and any other taxes.
Misleading prices
It's a criminal offence for sellers to give a misleading price indication about goods or services. That applies in whatever way the price indication is given, whether written in a notice or leaflet or given verbally. For example, you may see a price ticket showing £5 for the item, and then you're charged £5.10 at the checkout.
You have a right to claim back the money you paid to a seller if you bought the goods as a result of the seller using misleading of aggressive sales tactics. For more information see the government guide on misleading and aggressive commercial practices.
If the seller prices a product with the wrong price in error, you can't insist on buying it for the displayed price unless the transaction has already been completed. The seller must nevertheless take immediate steps to correct the mistake.
If you order goods for an agreed price, the seller can't increase the price when the goods are delivered, unless you've agreed in advance that the price may change. If there is a significant increase in the price, you may be able to argue that this is an unfair term and you're not bound by it. However, you may not be able to challenge the price increase if you were given the right to cancel and you didn't act on it.