Are receipts required in law?
The law in the UK is covered by the Sale of Goods Act 1973.
The terms implied when selling to a consumer form a contract that the goods are of satisfactory quality and meet their description.
If the supplied goods or service are not of acceptable quality, there is the right to reject them (there is no right to an exchange of goods).
The Sale of Goods Act 1973 does not state that a receipt must be produced.
If there is a dispute the purchaser would have to prove to a court that the purchase had taken place. In that case a bank or card statement would suffice be a receipt.
If no receipt has been given, or can not be produced, the seller can not deny liability for the contract of sale, and may be covered in the Unfair Contracts Terms Act 1977.