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Sent "Signed For" (formerly known as "Recorded Delivery")?
Either way you'll have to refund the buyer and then claim compensation from Royal Mail, you can't make them wait until RM cough-up: you have sub-contracted your obligation to deliver the goods, which isn't the buyer's concern or problem.
Double-check but I'm pretty sure that if you don't send something Signed For, then even if RM accept your claim (which will take that much longer without a tracking ref.) your compensation will be limited to £20 and you will received that in stamps, not cash.
Using a service with some form of tracking or proof of delivery is a must IMHO: it's the seller's equivalent of Paypal's Buyer Protection.
Also be sure to check the amount of compensation offered: it can sometimes be cheaper to opt for a faster service (which has a higher limit as standard) than increase the cover on a cheaper service.
sold an item and sent it through a second class stamp, dropped into a post box. two weeks later, buyer didn't receive the item yet. what to do? he opened a case.