VAT Regulation 16 is the legislation which allows a retailer to provide a much simplified invoice to a customer. The main condition is that the total value of supplies is less than £250. And, you cannot include any exempt supplies on such invoices.
If you sell items at different rates of VAT you must show the gross amount due at each rate of VAT, and the relevant VAT rates. You do not need to itemise the VAT.
HMRC guidance is in Notice 700, para 16.6.
If you are the purchaser, then a retailer’s invoice is valid evidence to claim input tax. The invoice does not need to show your name and address.
And you work out the VAT using the VAT fraction. For example, where the value of the supply is £120, and VAT is 20%; input tax is £120 x 1/6 = £20.