If a business isn't VAT-registered there's no obligation upon them to issue a receipt for any transaction. If a retailer is VAT-registered they should provide a VAT receipt if asked to do so.
Retailers are free to determine which methods of payment they will, or won't, accept. Many small traders only accept cash.
I don't know that you have to, market traders don't issue receipts. My friend has a shop and only takes cash, none of the customers seem to mind. Depends on the shop I guess - if it were selling big things (or something you might want to take back if it doesn't work) I wouldn't go there, without proof of purchase.